Western blotting with multiple antibodies
What you can do depends on your proteins: If both proteins (your target protein and the loading control) are seperated far enough, you can detect both of them in the same step by adding both primary antibodies and both secondary ABs into the buffer at the same time. They will bind only to their specific epitope and you will get nice signals. This is something I have done several time. This avoids the stripping process (which can be tricky sometimes) and you have both signals on the same film. Additionally you save chemicals, film and time.

There is another way with which you can come around the stripping: Do you first primary/secondary antibody combination and then incubate the blot with a buffer containing sodium azide. This inhibits the enzyme irreversibly, you have to make to wash very carefully afterwards. Then you can proceed with the second antibody combination.

If you want work with a marked primary antibody (which is unusual, but will of course work) and your loading control at the same time, I would definitely make sure that the secondary antibody with the HRP is not binding to your marked primary, otherwise the signal might get very strong (from the primary and also from the bound secondary), but I don't think it would cause other problems.