The AM62xx probably does support peripheral-level timestamping, which is what you need for AVB. However, there's no ethernet port on the PB2, so you can't really access the ethernet peripheral in the first place. If you are planning on using a USB-ethernet adapter, then you should check whether that does support timestamping. The real-time implications of all of this are of course pretty important: going through the USB stack bypassing the Linux kernel (e.g.: with Xenomai) is quite a task ...
OTOH, I like to think that if you have linux-level timestamping you can still get AVB to work, just with more jitter.
What are my options to adjust for clock drift on Bela?
You can in principle tweak the TLV320AIC310x's PLL via PID, but that may yield nasty sounding results (the PLL is not really meant to be adjusted while the audio is running). Software resampling may be the best option in practice.