Absolutely, but I don't think it should come down to one person to initiate it all.
I think my ex and I hit a perfect balance when it comes to this, at least I think so. She messaged me saying that she liked me and that she became quite close to me after we knew each other for half a year and skyped a lot during the summer; then the following day I asked her out. The way I see, this involves equal risk from both parties. The first initiates but doesn't invoke a "rejection" phase where it's all or nothing, it's much easier to tell a person that you like them rather than go all out on a "wanna go out?" type of comment (this would be more of a leading question that would get a biased result, in a way). While the second party either builds much more confidence to ask them out or can easily reject them without hurting their feelings too much. The only issue I can see with this is that messages may be misinterpreted when a relationship is not intended.
This also helps determine if the other party genuinely wants a relationship with you because you hear it from them about it as opposed to blatantly asking them out and if they say yes it doesn't necessarily mean they would really want it. I would be much more relaxed about it if I'd be shown interest from the other person, knowing that they are prepared to put the effort into it as opposed to initiating everything myself.