Honestly, it would seem to me that you might first take a moisture reading on a few other wood pieces within the same room if possible, but at least within the house that it is in. Once you have an established MC for what's in the house already, then test the table top and compare. If it's within roughly a few percent difference, fill what you've got and proceed with enjoying it. If not, it really depends on just how far apart the measurements are. If it's roughly 6 percent different, I might be inclined to leave it alone until it has reached EMC (equilibrium moisture content) and then fill it as suggested. The further away from EMC the piece measures, the more likely it is to continue on it's present course or worse.
One of the things that happen quite often in my shop is when flattening a thick piece of wood >1.25", no matter what the MC of it is initially, it will generally read differently once you have removed a quarter inch or so of wood from its surface. Like others have mentioned, it should be allowed to dry out more before further processing as you have now opened it up to different stresses, and when drying can begin to move in whatever direction has the least resistance. That could be splitting, cracking, checking, warping, twisting, etc. I will let the wood dry again after flattening to assure that it has at least reached EMC or lower before I proceed with making a finished piece out of it.
Whatever you wind up doing to the crack, I'd definitely suggest finishing the bottom with a clear coat to help prevent moisture issues in the future. When I was first researching finishes many years ago trying to learn the properties of them and what would work best for sealing wood, I settled on Zinsser's Seal Coat, an unwaxed shellac, as all the research at the time pointed to the fact that it was superior in limiting the transfer of moisture through the finish. I have for 11 years now, applied it to all surfaces of furniture that I build. Some pieces, such as table tops, also get a finish over that on their top surface for protection from spills, cleaners, etc. I have built some pieces with wide (20"+) planks in them and thus far had no issues.