I was thinking more the other direction. Corruption acts as a additional barrier to entry (will I get that contract? I can try and pay more money/bribe the right people, but even if I do that maybe there's a family connection I don't know about). This reduces competitive pressure, making monopoly more likely.
I'm not sure that increasing competitive pressure would decrease corruption. I can see how it might help, but it might also hurt.
e.g. a previously minimally corrupt business owner finding it harder to compete succumbs to temptation to join in the game due to increasing competition. So I think that part of it could go either way.
Africa needs more cell phones.