Can Testcomplete be used for verifying a 3-tier architecture web application?

Test complete is GUI functional testing tool.

It has some extra capabilities like calling database and web services.

But for load testing and stress testing can not be done with TC.

TC can drive it's sister products like SOAPUI, ReadyAPI, LoadComplete.

and could be integrated with some other tools (eg Jira)

To manage all tests I thing better to use test management tool like QAComplete, HP/ALM or Zephyr.

all depends on what your product , what you need to test, what tools already used and your budget