I've arrived twice IFR. It's not that big of a deal, though you may end up parked long enough to get your reservation. In actuality, not too many people avail themselves of IFR arrivals at OSH.
Of course, I hit there two days before the NOTAM went into effect a few years back with this exchange.
27K: looks like the clouds are closing up at Oshkosh. Can I get a clearance from you or do I have to go to FSS.
MKE: [SIGH] (he literally sighs over the air, like, crap it's starting already). Are you rated and equipped?
27K: affirmative.
MKE: Navion 5327K is cleared direct Oshkosh. Expect the VOR 9 approach.
27K: How about the RNAV 9?
MKE: OK expect that.
Interesting busting out of an 800' ceiling to the show.
LOL. I love the (sigh)...
I used an IFR to get OUT once, and that worked great. Slot time from the iPad the night before, and cranked and off as the first departure off of 9 the next morning. It was a Thursday.
Raising clearance delivery/ground was entertaining. Someone further out in the N40 had a slot behind us and the controllers obviously couldn't hear him calling. Two or three of us were fiddling around relaying for him so he could get his start up clearance. A few minutes later, a voice from ground who had "been there done this" finally just announced, "All aircraft with IFR slots, start engines and follow the flagmen to runway 9... if you need something else, call us again. We'll call you with your clearances once you're in a better spot where we can hear you." The old guy knew what was up. Heh.
Nobody expected anyone to be going anywhere in the low weather, so vehicles were dropping off volunteers with flags in front of us all the way to the runway from the north 40. LOL. Follow the flagmen... as they hop out of that pickup truck in front of you. Haha.
Overcast layer lifted as we were taxiing so it could have been a VFR departure anyway, or barely, but was kinda nice to get going when we needed to get going, either way.
The usual line of camera ships and performers going up to shoot morning air to air, had all bagged on it for low clouds. With the clouds having lifted, I had time to wing wag bye-bye instead of transitioning straight to the six pack.
I even had time to do a mini run-up while waiting for the pickup truck drop offs. Figured I might as well while watching the poor volunteers scramble out of the clown car... haha. At one of the stops the ground guy was obviously watching with binoculars... "Cessna 79M, got your IFR clearance, when ready to copy..." Sharp dude.
I got to be everyone's alarm clock in the North 40 that day. Fun.