My answer to this question is a no. If you were in a relationship with someone and it was just sex, that person more than likely lacks the honesty and integrity to have a real relationship which is why it was only sex in the first place if it wasn't your idea. This may seem biased but I got seduced into a full blown relationship that was supposed to be just sex and it turned out for the worst in the end. Although I do question the mental stability of the person I dated.
I'm not saying there is a 100% chance that the relationship won't work, but I am saying there is a gigantic risk factor to think about when you make this kind of decision. There is an extremely small and diminishing amount of faithful, honest females remaining on this planet especially in the United States and the percentile continues to decline as many women give in to greed. I am in no way sexist but I have lived it, and witnessed it being done to others.
All in all I would not advise you go through with a relationship with someone who you were "just having sex" with. I also would not advise you go through with a relationship with someone who had sex with you on the first night as that says a lot about how easy it is to sway them. If they did it with you, why wouldn't they do it with someone else? As humans we always think we are the most important person on the planet, but the truth is there are millions if not billions of people out there just like you, you're not special, and the chance of them doing it with someone else is very significant.
The choice is yours, just choose wisely.