When I lived for a short time in Oklahoma City, yes it was majorly important but this was in 1985 when the big am’s were still in power. The big am there went wall to wall with coverage. I can’t even remember their calls but I do remember their coverage of such. I would guess most today get phone alerts.
I grew up mostly in Texas and Oklahoma, and, today, OKC radio stations simulcast TV audio. I don't think any of them do their own weather coverage anymore.
Tulsa has always, in my opinion, had better radio severe weather coverage than OKC, despite OKC generally having worse weather. With two clusters in Tulsa being owned by TV broadcasters, you'd think you'd hear more simulcasts of TV audio, but at least KRMG and the Cox cluster originate some of their own weather coverage. They do have some cut ins and interaction with KOKI Fox 23, but the airstaff covers the weather as Fox 23 goes to visual focus. I'm not sure how Griffin handles severe weather coverage on its radio stations, though KHTT, at one time, did an excellent job at such coverage. KHTT is, or at least was, the LP-2 in Tulsa and always took that responsibility pretty seriously during the Renda era.