No, they almost certainly won't. As long as they don't try to intermingle the company's finances and/or corporate structures, anti-trust laws are unlikely to forbid one company buying a controlling stake in another.Antitrust regulators can block this kind of thing, also.
Typically, yes, that leads to a merger. But not always. If you want to see an example of this, just look at Match Group. They own nearly every single online dating service out there via stock ownership, but no one does a thing because each service is "independent".