Chris:

No it is not allowed to have finished (painted, varnished, or oil finish) in the machine room.  The main reason for this is that in addition to impacting the tools (blades, bits, etc.) is causes havoc with the dust collection system.  So your best approach would be to remove the finish first with either a chemical stripper, or through sanding.  Be aware that finishes can contain lead or other chemicals so if you are sanding use appropriate caution.  

If you do bring unfinished recycled wood into the shop we also ask that it be scanned for any hidden fasteners.  There are metal sensing tools in the shop for this purpose.

Paul