Yes, but: nuclear weapons in space are prohibited by at least two treaties to which the US is a signatory; any point on the globe worth hitting with conventional weapons would be far easier and cheaper to hit with, say, a cruise missile or a drone-launched Hellfire; last but not least, you'd first have to build a weapon to fit in this thing's cargo bay, which almost certainly has not been done because, given the first two mentioned points, it's not worth anyone's time or money to bother.

To understand the X-37, you need a reasonable knowledge of the origins of the Space Shuttle program. The only reason that program came to even the bastardized fruition it did was because the Air Force signed on, and they did so only because they needed a means of servicing and maintaining their orbital equipment. In theory, and occasionally in practice, this means involved actual human astronauts going up and doing spanner work on satellites in orbit, but this was expensive and fraught with undue difficulty; cheaper and easier was simply to stuff the whole satellite into the Shuttle's payload bay and haul it back down the gravity well for repair, refit, and relaunch, and indeed many Space Shuttle missions involved precisely this evolution. (It's probable, if uncertain due to the Air Force's bent for secrecy with regard to their payloads, that the Shuttle was used to return some or most of these satellites to orbit; on the other hand, a Titan-IV's probably cheaper, and the Air Force has used plenty of those, too. I don't know much about what goes into that sort of decision.)

The X-37, then, far from being some kind of conspiracy-theory FOBS, is just a Space-Shuttle-style "space truck". The major difference is that technology has now reached a point where it's possible for such a vehicle to satisfy the Air Force's mission parameters without having to involve all the complex, costly, and potentially disastrous encumbrances required to carry living humans into space.

Edit! I've finally just recalled the name of the book from which I gained my understanding of the politicking which took the Space Shuttle program from initial conception to final operational "Space Transportation System". That book is The Space Shuttle Decision, published by NASA as part of the NASA History Series, and you can read it online at http://www.nss.org/resources/library/shuttledecision/ and, oh, probably lots of other places as well. A bit dry, but marvelously detailed and surprisingly objective given its origins; I recommend it unreservedly to anyone with an interest in the history of its subject matter.