That would depend if the wired traffic is being routed to the wireless network. Only you can answer that (since you set the networks
If you can ping the wireless printer's IP address from the wired PC, then there is little likelihood that there will be any printing issues. If not, then some accommodation need be made (what that is depends on your comfort level, willingness to change setups, and/or capabilities of networking equipment).
In my case (where the wireless network cannot be access from the wired side), i put the printer the the wireless network's DMZ, on the wireless router. This made the printer appear to exist on the wired IP address of the wireless router...