I haven't done it. However, I do have a couple ideas that you can explore...
Tableau now has the ability to read JSON files, so if you can find one of the applicable server log files that has the needed info in the right format, then this may be a good option
There's also used to be a JMX MBEAN that you could monitor with TabMon which would report # of attempted logins and # of failures. Do a touch of math and you know how many successes you have
It was webclientappservice.login and the counters were RequestsFailed and RequestsProcessed.
I THINK these got moved around a bit between Tableau 9 and 10, so you'd have to dig for them a bit. This link might help: The new (and fiendishly hidden) Tableau Server monitoring improvements in 9.3 - Tableau Love