Not unless Romney paid them a bunch of money to play it. Even then, I find it highly unlikely they would play Romney's inauguration, simply because they have no ties to him (that I know of) and likely he's not as big of a supporter of aiding Africa/other countries. If he were, maybe because Bono's all about the politicians who support/aid his work in Africa (just look at Bono's relationship with former president Bush).
Now if Huckabee were to be elected, I could see Bono maybe showing up at the bash because they seem to be chummy and Hucks repeatedly dropped Bono's name at the RNC last week.
Regarding Obama's re-election hopes, Romney, imo, isn't a strong enough candidate to defeat Obama. Unless America really is too dumb to fact check and learn more about what both candidates bring to the table, I highly doubt Romney will be elected. He's too unlikeable (where are those tax returns?!?), flip flops too much, lies too much and has yet to provide a solid plan for how he'd turn things around.