Do you leave 25B AIT or Signal BOLC with IT certs?

That is true, you don't actually get to take any certification tests in the course, as this is an MOS school, not a CompTia course conducted by civilian entities. At the completion of 25B, if you paid attention, you are relatively prepared to pass Network+ and some Cisco tests. You can do that on your own, or take the classes on post at an ed center (active duty) or NG PEC (Guard) to get the voucher from the class for the tests.
Moreover, with the MOS, you now have training and job experience to add to your certs on your resume. Companies are looking for both certs and experience when they hire.

If you go to SBOLC then you have the opportunity to take the Network+ cert exam as well as the Security+ cert exam however, in my experience, the test dates were WHILE we were still learning the curriculum so you have to either be proficient in the subject before they teach the information or you have to be highly motivated and self study.