I have 2 spawners 63 blocks apart. I want to create a cart network so that I can go front and back from a spawner to another for them to work in my xp farm since the spawning radius for a spawner is only 16 blocks. Will this work?
Yes you could do this, but it would not be efficient.
In order to activate the spawner, you need to be within 16 blocks of it. If there are 63 blocks between the spawners, there will be about 31 blocks of travel where you will be in neither's range. No matter your speed, there will be some loss. It would be better to just use one spawner (on hard difficulty to maximize drops).
For other's looking for this, the only reason to farm with two spawners is if they are less than 32 blocks apart (3d distance) so you can activate both at the same time.