Hi Nicola,
I think that you need to think about 2 things here before you go ahead with this:
Firstly, I would definitely class this as grey hat. It could be said to be a mild form of negative SEO. I don't quite know how your users would feel about this as well, because many people will actually see right through this. As well as this, if you are going to try and outrank your competitors for their own brand name, it means that you are going to be competing with their homepage, which is likely to be extremely difficult seeing as you will have a hard job getting links to your 'competitor brand pages'.
Secondly, it is worth thinking about how this will affect your brand. For example, if a user enters your website through another brand-name page, it could provide them with a lot of confusion, and this could lose trust with your customers.
Personally, I would stay away from this tactic, as you have much more to lose than gain in this kind of scenario.
Matt.