Yes, it's a good buy and a good bike. My wife is also 5'1" and our stoker seat tube measures 18.5" from the center of stoker's bottom bracket to top of the seat tube. She still has a few inches of seatpost showing.
Since you've not ridden a tandem, I'll warn you that a tandem does not handle like a single bike. It'll take a little time to get used to it. Also, many tandems do not handle at all well without the stoker on board. Their steering design assumes the presence of the stoker.
Before your first ride, it'd be good for both of you to read about The Proper Method:
The Proper Method
The most important thing for the stoker is simply to sit quietly, not attempt to balance or affect the motion of the tandem at all, but rather just sit still and pedal. My stoker says never look up the road, you'll anticipate what's going to happen and you don't want to do that. We find starting to be easier than on a single bike, but stopping is trickier, getting the bike to lean just so to enable the captain to put a foot down. It's probably best to practice in an almost empty parking lot so you don't hit anything while getting the hang of stopping and starting. Under way, a tandem is very stable and comfortable.
If it turns out that you like tandeming and get to hankering for a ligher, more modern bike, don't try to upgrade this one. Just buy a newer used one or even buy new. We bought a very nice used tandem in '07 and seldom ride our singles outdoors anymore.
If you will be riding on pavement, you'll find those tires will be slow. For the road, choose smooth tires, or as smooth as tires for those rims come. Continental Contact Speed tires should work well.