Just weighing in here! My (US) partner (UK) and I have been visiting each other back and forth for years at this point, but he just visited for a 3 month period and the VISA application did not come up at all in customs. I know that's a big worry that TSA will see your pending application and not let you in, but it wasn't an issue.
He however WAS taken into secondary interrogation and was VERY close to not being let in the country because they were suspicious of him trying to live here since the stay was long. They searched his bag and thought because he was bringing his laptop for gaming that he was actually trying to work here. He's self employed as a carpenter back home and works part time in a bakery as well, but they didn't really believe him when he explained how his range of income varies dependent on his work, and I also suspect that they took his self employed situation to mean that he didn't have strong enough ties at home to go back.
I'd say even if you do have the ability to visit for longer periods, it's probably a lot safer to keep your visits short while your VISA is processing. But all this to say, my fiance was let in the country and we enjoyed our stay. It IS possible to visit.