I would say nay, for a number of reasons.
Let's take the somewhat sunshine scenario first. You make something that actually succeeds. You start earning a lot of money. Has each of you contributed as much to the outcome as the other. And will both of you say so about a person they have only met online. Prisoners dilemma. Or at least could be if one decides to screw the other. And I think every piece of research ever done about behavior online points to the fact that people are less empathetic towards each other online.
Second point: I have started to believe that the most important factor in any endeavor, whether it being starting companies or otherwise, is to do it with people you really enjoy spending time with. Whether you succeed or not you have to make the journey, that journey might as well be with someone you really like.
You can of course find someone online that you end up really liking, but I would advise against a "fully remote" relationship.