The problem I see is that its difficult to get the ball rolling.
Its not minor tribes that they'll be dealing with. Much of West Africa had small but well organized states that were an insane pain in the ass to keep in check when you lack modern technology such as the machine gun or medicine. And then there's the Sahelian States that were no pushover, even after the Fulani Jihads. The British in Nigeria adopted the princely state method of control for a very long time for good reason.
This company isn't going to have firm control even with boots on the ground without full on government support, and that requires a 'Scramble for Africa' scenario, which would hurt any company that seeks to go the East India route. They'd also be short on recruits as up until the late 1800s the only areas really suitable for European settlement is the Sahel, and that was seen as marginal land at the time. You could speed up the settlement of the more tropical regions by introducing Quinine into there (that's been a malarial treatment since the days of the Inca) but still, its very difficult to get many immigrants in the region. Instead it'd be far more cheaper to higher natives to work in the bureaucracy or as soldiers, which has the benefit of being relatively common in pre-colonial Africa when migrating ethnic groups establish themselves as the new ruling class.
All in all, this will be a highly expensive affair and won't see suitable returns on the investment until much later, which will dissuade its growth. However, this can be somewhat mitigated by seeing the company do what most Europeans did in India during the 1700s: Small to medium sized areas under direct control (mostly trade posts and what not) with large amounts of vassal states.