Is it okay to join a self-funded PhD Program with possibility/intention of leaving in future for funded position
The only ethical concern here, hence the only thing that would make it not ok, is if your leaving breaks commitments to others and leaves them hanging. This might happen in some lab-intensive fields where your research dovetails with that of others. In that case you would need to clean up the situation, but still aren't obligated to continue forever. 

Most people will understand your situation and your desire to move if you do. I don't think that obtaining letters will be a problem as long as you fulfill your obligations. If you are doing good work, there may even be an incentive at the first institution to find funding for you in some way. 

The only negative I can see is a question might arise about why you can't get funding. Is there some deficit in your background. That might make it harder to get accepted, but otherwise I don't predict any  issues. 

Actually, people leave funded positions as well. The same basic rule applies. Fulfill your obligations and don't leave others hanging. Laws and contracts may modify that rule in some situations, of course. 

Joining a doctoral program isn't a one time, irreversible, life-time commitment.