It doesn't affect vaginal birth - but it can make it harder for baby to engage if the tummy muscles aren't holding him in over the pelvis so he can push on the cervix itms. i strapped my tummy day and night for the last few weeks trying to give bub a bit of stability in there. this was 2nd pregnancy with 2nd large seperation though.

i reckon recovery would be harder if you had both c section damage and tummy seperation at the same time. definitely go for supportive recovery shorts if you were in this position.
Just a note that some physio's will recommend wearing a support belt for as long as you can during labour if this is the case... or until you feel that bubs has definitely engaged. Thankfully we didn't have to do that because the feeling of having something on my tummy was so annoying!