As someone who was on the receiving end of a chronic texter, I can tell you that it will paint you in a bad light.
I went on 3 dates with a guy, and I cut off all communication as he was firing texts off like a machine gun. Before I was able to reply to his first text, I had 6 or 7, as you crazy kids say "blowin' up my phone". Plus he also had no regards for time, as he would text me late into the evening.
I had to turn off my phone at night, despite the several times I told him to not text late.
We had a falling out, due to other things, he still continued to text, which I never responded but he finally got the message after the 3rd week.
Don't become this guy.