Maybe but I'd think not as bad as comm. radio can be. It still would be dependent on private contributions as well as foundations and corp. donations (announcements of which are publicity which can serve as advertising and I think it's a tax writeoff).
An understandable misunderstanding. Donations to radio stations only apply if the station operates as a non-profit. Non-profits cannot run commercials (that's both an IRS and a FCC rule) so if the concept of NCE broadcasting were ended and all public radio stations suddenly because commercial entities, then donations to them would no longer be tax-deductible.
The esteemed Bob Bittner has this issue; donations to support WJIB are NOT tax-deductible, although he provides compelling content for a large enough audience to support his little operation so he makes it work....but that model would be damn hard to export to the industry writ large. Remember, AFAIK Bob only has one employee to pay for: himself!
Anyways, losing the tax-deductible aspect would be devastating to public radio stations. Not so much for the average donor, they'll give regardless of the tax issues. But it would remove a significant incentive for the major donor. And major donors are a huge part of the successful public broadcaster's revenue stream. The average, everyday donors are the bedrock that a good station builds and that convinces the major donors of the "seriousness" of the station, and thus provides a path for major gifts. Same rules apply to most gifts to higher education, too. Your alma mater doesn't really care much about the $100/yr you donate. They care that 10,000 of your fellow alums all do the same, so that they can qualify for a matching donation from one rich fatcat alum. There's a ton of research into the psychology of both minor and major giving for charitable institutions out there, and a lot of it for public radio at DEI, although most of the DEI stuff is behind a paywall for their clients. What's available is still good reading, though.
How much does this apply to WBUR, for instance? Their pledge drives constantly tell me how little comes from the government. The people who argue against ending supports make a point to state how little of the public radio stations budgets come from the government.
This gets into the big vs little guys in public broadcasting. You are correct that the Top 20 or so RADIO stations (TV's a different beast)...like WBUR, WAMU, KQED, WNYC, KERA, KUHF, MPR, etc...would only feel a minor pinch if all federal funding (e.g. CPB) were cut off tomorrow. Most already don't have any state funding, either. These guys already have such huge budgets and titanic earning power that even the CPB multiplier formula for the annual Community Service Grant only makes up a small part of their total budget. It'd suck to lose that "free money", and it might stifle innovation and new ideas somewhat, but it probably wouldn't result in major cutbacks. For these guys, the killing off of the PTFP program was much more painful, as that was a fantastic way to implement major equipment & facility upgrades; PTFP covered 70% of the costs of many of them.
Then there's the middle ground that probably could survive losing all CPB funding, but it would hurt. Mostly the Top 20 to 50 markets. You'd see layoffs and ending of certain services (mostly local content, probably). There'd probably be a couple that would, by luck of the draw, also be nailed with some other financial hit at the same time and be forced into major changes and/or shutdown. But most would struggle on...it's just that the margins would get razor thin and/or they'd make significant cuts to be solvent.
Below Market #50, the loss of CPB funding starts getting devastating. These guys often (not always, but often) have comparatively small budgets...less than $1mil/yr of gross revenue. (which ain't much...five FT staff at a measly $40k/yr salary costs the company about $250k in payroll/benefits costs alone) At that level, losing the $65k to $125k of CPB funding is a major bite. Most of those kinds of stations only have the minimum of five full-time staff to begin with, so there's not much to cut. Worse still, many are owned by, and based at, colleges. Colleges that may already be wondering why they have a radio station that doesn't benefit the students, isn't improving alumni donations, and could still be worth a few million on the open market...and now suddenly might be coming, hat in hand, to the college to help plug a big budget hole.
Finally, let's put this in perspective. WBUR is one of the top earning public radio stations in the entire country. It's also one of the top-ranked stations in Boston in the demos that matter. And yet their annual gross revenue budget is, IIRC, under $25 million/yr. It might be under $20mil at this point. That's a pretty low dollar value compared to what the top-earning and top-rated commercial stations are. Heck, in 2006 WEEI 850AM was the dominant player it was (much like WBUR today), that station was pulling in $36mil in gross revenue BY ITSELF. Never mind the rest of the Entercom cluster.
Why the disparity? Commercial vs non-commercial is a big part of it. But really a major difference is just raw inventory. Most commercial stations run at least 15 to 20 minutes of ads every hour. WBUR usually runs maybe 4 minutes, tops. That's another reason why you cannot remove the non-commercial structure without dooming public radio to race to the lowest common denominator just like all the rest of commercial radio: the profit structure demands that much advertising time, and it's fantastically corrosive to the quality of the programming. As the saying goes, you can't sell just a small part of your soul.