You can use your tuner with most antennas I'd venture, so no reason why not with the hamsticks, however I'd look to borrow someone's analyser and make sure you get the antenna resonant first. The 10m hamstick is pretty much a 1/4WL antenna and will work very well indeed, the more loading you add to the antenna the less efficient they become, 20m being the breaking point, still reasonable efficiency.
Check out this mobile antenna shoot out and look what came second, but I doubt most people would drive around with this particular antenna installation:
2012 mobile shoot out
Check out this mobile antenna shoot out and look what came second, but I doubt most people would drive around with this particular antenna installation:
2012 mobile shoot out