Yep. I have a WRT32X, which I think is the same HW as a WRT3200ACM that is running multiple wifi networks and VLANs. Also have an older WRT1900acs that does the same. I am also trunking the VLANs over a couple other routers so the APs have the same VLANs. Most semi-decent routers even older ones support VLANs.
If you end up with a WRT3200ACM or the other similar linksys, check out David's specific builds for them. Davidc502- wrt1200ac wrt1900acx wrt3200acm wrt32x builds