The idea sounds good at first, but it will be problematic.
Guitar pickups produce a weak signal. The amplitude is barely sufficient to feed to an ADC. Therefore you still should expect to amplify it in the normal analog manner.
After that, you can feed it to a microcontroller. The ADC will turn it into digitized audio. You'll have to store each data value, process it, then send it to the DAC output. You'll have to do that tens of thousands of times per second.
If you introduce any audible delay, it will sound funny. You may find it is unsatisfactory with real-time performing.
You'll need to move digitized audio in and out of memory rapidly. Perhaps store incoming data in one bank, while moving it out of a second bank.
If your fpga can execute your code quickly enough, then you may find it easy to overcome these challenges.