With the added info in the comment, I'm going to say that it should be okay.
IFR. Runway is notamed closed until 1900L(our ops don't allow landing on taxiways if there are other options and grass is no good for a jet). Airport authority has said it will likely be open much earlier. Wanting to take off and hopefully it will be open by the time we get there.
My reasoning is: you can file to airport (A) that has an instrument approach that will get you down below the weather (say a 3000' overcast), fly the approach until you're in VMC, cancel IFR, and proceed VFR to airport (B), which is where you actually intend to land (but which has no instrument approach to get you below the weather -- and no radar coverage). This plan works even if airport (A) couldn't accommodate your aircraft for some reason -- runway closed/shortened, weight bearing capacity, whatever. (Obviously you'd need alternate plans if the weather didn't cooperate with going VFR from A to B, but let's assume that you have a place to go land and plenty of gas to get there for a case like that.) What matters is that you have an approach you can fly at Airport A, not that you can actually land there.
Worst case, perhaps you could file to airport A where you want to land, and then after that file routing to airport B which is where you'll go if the runway doesn't open up in time. Thus your filed flightplan is simply "I'll fly an approach at A then go land at B" and that's a perfectly workable plan even with the NOTAM as written. Then, in flight, if the runway opens early as expected, you tell ATC to amend your destination to airport A and you're all set.
Disclaimer, IANAL (I am not a lawyer), but this seems entirely workable to me. I know in the 121 world, we explicitly ARE allowed to file to an airport below our mins, with the hope that it comes up (better than forecast) above mins by the time we get there. It requires extra alternates and such, but just because we "won't" be able to land there based on things as we see them at this moment doesn't mean we can't be dispatched to go there. And if things get better (weather comes up better than forecast, runway reopens sooner than NOTAM'd), you get to do what you'd hoped for all along. Just have a sound plan for what you'll do in the scenario where things don't.