What is more annoying on a date than when the other person is text messaging their friends the entire time. A date is a time for undivided attention and continuously text messaging can be an effective way of ruining a fun night.
But then, how about if both of them busy texting. Not to other person but to each other? Awkward? I think it is perfectly okay if they feel more comfortable texting rather than eventually talk. A short film about awkward text romance.