It may depend on the rental company as well as the local office, as well as whether you're a member of that rental company's "skip the counter" program or not, and as well as whether you booked directly with the rental company or through a third-party site for each reservation.

I thus don't see how it's possible to answer it in general, except to say that I would suggest you make the decision before you drive out of the lot with the first car, ie go look at the first car, and if it's one you want to keep, go (back) to the desk and ask about merging the reservations and keeping the car. That's obviously easier if you "bypassed the counter" (because you're a member of their "skip the counter" program) and thus the only time you visit the desk is after you've looked at the car; it requires a bit more courage to return to the same person who just gave you your keys and say "oh, I forgot...".

I've never rented back-to-back for this reason. I've only rented back to back to max out partner bonuses, and in that case I didn't want to have the reservations merged or to keep the same car, since that would reduced the partner miles/points I would have earned "per rental".