They legally aren't allowed to check but if a staffer or politician recognizes someone's name and remembers that they met at a fundraiser, it obviously influences them, at least subconsciously.

I was never asked to; Congressional offices and campaign offices are supposed to be legally distinct, and that information would have all been held by the campaign.

That being said, once the sums you contribute get large enough you will almost certainly get to be known around the office -- either explicitly (e.g. the Chief of Staff tells all the people who handle correspondence "Bob Smith is a good friend of the Congressman's, if you find any messages from him bring those straight to me") or implicitly (e.g. the staff of the Congressional office notices that when Bob Smith comes in to meet with the boss he's ushered right in and stays for a long time). So large contributors' messages can easily get special attention, even without that kind of direct connection to their contributions ever being made.