Sure, it all depends on your definitions.
On TV, of course, the 8th Doctor only had one story, and the Brig didn't feature in it.
The novels, audios, and comics detailed a lot more of the 8th Doctor's adventures, and we saw him fighting alongside the Brig a few times, but they never regularly traveled together, so it comes down to what your definition of 'companion' is—and whether you count those stories.
Finally, we know the 8th Doctor had all kinds of off-screen adventures before the Last Great Time War, and the Brig could have been involved in some, or could even have traveled with him as a regular companion for a time. So, if you wanted to write a story where they're companions, there are plenty of places you could fit that story into both of their timelines without contradicting anything.