Does MEPS pull your military medical records?

Oh yeah and if you want to be in the Army, you should get familiar and start practicing the Army values... Start with integrity.

When military dependents enlist, they pull their records from TRICARE. So I'd assume they'd pull prior service too.

Yes, but you would be surprised at how many waivers they approve.
On the other hand if you were barred from reenlistment, medically retired or put out for an injury then chances are you will never wear the uniform again, although a good war makes most all of these problems disappear and they will approve all waivers at that point. During the surge we had everything from convicted felons to soldiers that were awol for years just show up during the deployment as fillers for the units that just needed bodies to meet mission parameters so there's always a way if you are serious and have a great recruitment center.