Short answer: No. Including a reason in a request doesn't make that request 'more assertive'.
I think you're mixing up two things here: assertiveness and asking for a favor.
First off, assertiveness (emphasis mine):
A form of behavior characterized by a confident declaration or affirmation of a statement without need of proof; this affirms the person's rights or point of view without either aggressively threatening the rights of another (assuming a position of dominance) or submissively permitting another to ignore or deny one's rights or point of view.
Assertiveness doesn't need proof. Assertiveness is being able to declare 'I'm sick' and 'I need more sleep' in such a way that people don't ask you to prove yourself, believe you, and are willing to accept your point of view. But it also means doing it in such a way that you respect the fact that your neighbors have a life too, that the walls are thin, and that total silence is not going to be an option.
It is true though that when asking for a favor, including the reason you do so makes people more willing to comply with a request, even if that reason isn't a good reason. There have been studies showing that someone breaking into a line of people waiting to photocopy something was given less resistance when they said 'Can I get ahead, I need to photocopy something' than when saying nothing at all. Even though 'needing to photocopy something' isn't really a reason to cut into a line of people waiting to photocopy stuff at all.1
So, to make asking for a favor most effective and to be assertive at the same time (from wikihow):
- Approach your neighbours at an appropriate time (e.g. not right before they have to leave for work, but when they come home).
- Tell them outright you're looking for a favor ("I've got a favor to ask of you")
- Then ask your favor. There's a few things you can do while asking, but the most important to keep in mind are:
- Be clear of what you're asking ("I would really like it if you could be a bit quieter outside my bedroom in the morning?"), don't ask too much (some noises will probably always be there) and also don't ask more after the first 'favor' has already been granted. If you could come up with some specific noises that bother you the most and that your neighbors can avoid making, asking them to avoid those would be even better than just a general 'could you be quieter?'.
- Include your reason for asking: You're ill and being awakened that early is bad for your health.
- Offer a reason for them to be quieter. What's the worst thing that can happen if they don't? Perhaps you'll only get sicker in the long run? Don't be over the top though, keep this real.
- Give them a way 'out'. This one is tricky for a favor that asks people to be quieter, but perhaps acknowledge that the walls are thin and some amount noise can't be avoided, show that you're understanding this.
The assertiveness here is in the use of I-statements. Don't say 'You need to be quieter' or 'Can you be quieter', no, let them know that you like them to be quieter by using 'I would like it if'. Say stuff like 'I feel worse when being awakened too early', try to avoid saying 'You're making me feel worse when waking me up this early'. The I-statements are much less confrontational and a better way to both state your point of view and not come across as aggressive.
1 Joseph DeVito, The Interpersonal Communication Book, Global Edition (15e), p244