If you mean wearing the costume in public during a convention, yes, it's ok in big conventions. If you're going to little conventions or in little cities it's a common thing being watched awkwardly, but normally nobody would say anything strange xD
If you mean dressing up or putting your costume on, well it's a little bit weird. Normally when arrivin' at a convention you already put the costume on. Because it's really rare to find places where you can put it on during a con. Like dressing rooms or such.
Is it also normal to go around in cosplay during the convention even if you're not partecipating to the contest. Since the places where you can shop in a con are different from the places where contest cosplayers are, it's easy to go around shopping as long as your costume is comfortable and not really big. The space between the stands is really cramped sometimes...
Well of course anime and games are really popular! Even if you choose a really unknown character and cosplay it on really big convention (like Lucca Comics and Games o Romics and such) there's ALWAYS someone who will recognise you!
So don't worry! we have otaku here too!