No I don't think so, you are only available as much as u are available. Maybe it is just a bad habit of his and it also sounds like he is quite keen.

Maybe just try giving him the hint like when u reply back to one cut it off by saying I will text u tomorrow have a great day etc and if he doesn't get the hint just tell him honestly what terms u are willing to live with, i.e go slow etc etc

ETA. Good for you that u have found a possible relationship I hope it goes well for you