If you put long tube headers on, you have to remove the primary CATs and the LTHs won't fit otherwise.
If you still have your secondary, keep those as you state.
Technically, it shouldn't pass the visual because you are missing the primaries (and a tester probably know they are normally there) but it depends how jobsworth they are (they will see the secondaries and be OK with it, or, they can see you are missing primaries and fail it), and whether you pass on emissions which you should do with just secondaries as has been the case for others.
Secondaries are there to heat up the exhaust gases quicker and make the primaries work more efficiently but they are enough to do the job alone.