It won't weaken your application per se, but you're laying your cards on the table immediately as someone who's only interested in the flying, and has no interest in the service which allows you to do that.
So, look at it from an interviewer's point of view. I'm about to offer you a place to go through 9 months of officer training before embarking on a 5-odd year long programme of flying training, where you will be rigorously assessed at all times and monitored and checked all the time. There's a well known saying in the FT world that "you're only ever 3 trips away from a chop ride," meaning that a slip below standard in one sortie can start a snowballing process that ends up with you chopped within a week.
There are no guarantees, and plenty of people with decent aptitude run into capacity walls at various times and end up removed from training.
Now, let's say I have 2 candidates. You're one of them, have high aptitude test scores, an application in to the Navy as well as a pilot, pilot's your only RAF choice, and you've indicated in your interview that if unsuccessful you would continue with your Navy application. Then I have another guy, similar sort of scores to you, but he's got pilot as his first choice, then WSO, then ATC officer, then logs as a non-aptitude branch, and indicated in his interview that if unsuccessful he'd also consider WSOp.
Who do you think I'm going to take the risk on? I have to worry about what you'll do if you're removed from training after 2 years. Will you stay in the RAF to give us some return for the investment? Or will you be straight on the phone to see about moving across to the Navy to give their system a try instead? Even if they won't have you, the "pilot or bust" attitude would make me seriously consider your value if you don't end up in a flying job. Perhaps you'd be straight off to OATS waiting for an upturn in the commercial world?
Now, in a world with lots of slots, we'd take you both on and accept that there may be a risk that you wouldn't consider another branch if you failed flying training. If I were the President of the Air Board, and I only had one slot to give out, I'd give it to the guy more likely to stay in my service and provide me with a capable officer, rather than the guy who's only interested in being airborne.