Thinking some more about this, an interesting dynamic would be set up to where different powers from the Trek universe may end up wanting to also invade the SW universe. Specifically the Borg, but I'm sure others would be interesting in exploring/conquering as well.
If the Federation were truly committed to closing the wormhole; this could create in-universe fighting between Federation and those opposed to closing. Depending on how out of hand it gets you could end up seeing an Empire/Federation team up. Empire realizing they are over their heads surrender to the Federation, offer their ships, clones, droids, etc while the Federation shares Trek Tech.
On the other hand, you could have other factions using the Empire as pawns. Basically agreeing to an alliance in order to distract the Federation from closing the wormhole. Then once the Federation was beaten back enough, betray the Empire and take over the SW universe.
If things played out straight Universe vs Universe. Trek wins.
Empire + anyone but Federation. Empire Loses, Federation loses temporarily, but aren't destroyed or anything.
Empire + Federation. This would either end in status quo (wormhole gets closed) or the Empire turning around at the 11th hour to betray the Federation. With beefed up resources and Trek Tech, the Empire may have a shot of overcoming the Federation forces. Plus since they are no longer the weak force (har) they can't be set up as pawns for another faction to take them over. They could be equal partners with say the Romulans and run roughshod over the Federation.