I put in a 3rd gen game when I want to switch the delay, from odd to even or even to odd, yes. It might make you have to adjust Pikatimer again, but that's about all.
You may get a frame of 1, 3 or 5 on a different year. Also, you may not have your delays high enough to see the odd frame delays. If you're using Pikatimer, you can go much higher on the delays. I think you can do this as well if you use Emloop, which is another timer.
However, you can successfully RNG an even frame by simple getting down to two eggs, rejecting one and taking the last.