If you don't want a submit button to get in the way, then I'd recommend making it just an icon (like most text messaging apps). You can also only show it when the user focuses on the input box to simplify the initial UI even more.
However, we don't really know the context for why a submit button would get in the way of your UI. If you can fit it in, then do it because of all the UX and accessibility goodness you get with it. If not, it's not the end of the world and I'm sure any user would be able to figure out to press enter. If you're able to show a small hint somewhere to let them know, that'd be best.