There are two ways to view this question - one of of which is covered very well in the other answers and that is that you should avoid making a windows app look specifically like an OSX app.
But perhaps the question should be this - Is it ok to make an application on Windows look less like a windows app?
In which case you might lead on to ask: "Well what is meant by the look of a Windows app". To which one can only answer based on what the majority of users on Windows are used to. According to AT Internet and several others on Wikipedia, Windows 7 and Windows XP are in roughly equal use, each of which has about two and half times as much prominence as Vista. Thus it's not unreasonable to say that the following snapshot of XP is going to be pretty recognizable as Windows.
However, more and more software developers are wanting to target both Mac and Windows - and maybe Linux as well and hence cross platform toolkits like Qt (which also caters for some mobile platforms) are being used. By default Qt takes on the native look and feel automatically, but also allows customisation via CSS so that the same appearance can be used on all platforms while still using familiar OS dialogs like colour choosers, file open dialogs and the like.
This approach neither tries to make an application look like OSX on Windows nor like Windows on OSX, but allows the designer to create an interface that is a happy medium between the overly colourful more saturated hues of Windows and the more consistently designed reduced palette that OSX users are used to.
So you can quite well end up with nice looking applications like mFlow (below) which looks nothing like a traditional Windows app but has no problem fitting in. Similarly for Spotify which was also mentioned elsewhere who I believe developed their own cross platform GUI rendering toolkit. Skype is another application that has totally removed it's appearance from that of Windows to form it's own brand and identity.
I think the drawbacks of trying to do this then come from the potential to not do the job properly - or not considering the bigger picture. If you remove yourself from the notion of making a Windows app look like something else (OSX) and providing you don't just do half the job - making a Windows app look like a Windows app that's trying hard not to look like a Windows app (!), but instead you actually style the whole application to make it look better then there's no problem at all. That's so long as it befits the purpose of the application in the first place of course - that always takes priority.
Look at it like this :- If you're going to a top fashion event, don't just rely on a haircut to make you look good - dress well, choose the shoes carefully and clean your fingernails...!