Mister Geezer
Obviously it's up to the crew if they want to ask; speaking from an ATCO point of view, I would hope that any ATCO worth his or her salt would say 'no' to the request if it was apparent that there were aircraft ahead that meant anything gained through high speed (however slight), would be negated by vectoring for streaming purposes.
The short answer still remains, 'no, asking is not a probelm'; especially if tied in with the initial call onto the frequency - it won't take up any more R/T time
