If one were to use the washroom before davening and wash does that work for the tefillah following or would one have to say Asher yatzar and then re wash?
If he is davening right away he does not have to wash his hands again. The reason that we wash our hands before davening is to ensure that they are tahor and clean. Technically, if one would wash his hands even a while before davening and he made sure to keep his hands from touching anything not tahor he wouldn’t have to wash them again. This is not common, therefore we have to wash our hands before each tefilla, unless we are davening two tefillos together, (i.e. shachris and then mussaf). In your case he is washing his hands and then davening, so his hands are now clean, and there is no need to wash them again.
This is in contrast to washing hands after using the bathroom right before washing netilas yodayim for a meal, where the Shulchan Aruch says that he should wash is hands,say asher yotzar, make his hands tameh, and then wash them again. This is because he has to say asher yotzar, and he shouldn’t say it between washing his hands and saying al netilas yodayim. When washing before davening we don’t make a bracha, therefore this idea wouldn’t be applicable.
Shulchan Aruch 165-1, 92-5, M:B 165- 2, 92-23, 24, 25.