I think it matters a lot more for commercial mortgages. In any event, it's like 20-30bps or less according to the Fed. So higher, but not that much higher even for commercial mortgages, and even less for residential where there's a lot more federal protection going on.
The bigger impact, I believe, is that housing prices can go more crazy. People will take more risk if they know they can walk and leave the bank holding the bag, so there isn't that limiting factor on prices.
(Though I suspect, but obviously can't confirm, that the effect from non-recourse mortgage is absolutely dwarfed by other factors, especially out here on the west coast where we have very restrictive zoning policies, weaponized environmental policies inside urban areas, etc)