Google likely won't allow that under any applicable trademark law or policy. So short answer is no, especially if they have an office in your area. Lots of examples out there, but a recent one is where they sued a Dutch man for having done so.
No, unless you want to get a potential lawsuit from Google. Why would you even want to reg a name like that in the 1st place?
dont buy google like domain I have googledaily.com, such domain can get closure notification at anytime and you will loose your traffic n site recently Google blocked adsense at my domain because of trademark infringement. but they didnt sent me any warning to close the domain and thanks God they have not disable my adsense account. working well at other domains. Now Im using it until they contact me to close it. But I suggest you never to take domain having trademark registered ..