I don't really think it was ever a serious plan, or if it was it would have been a Children in Need-style spoof. For one thing, RTD's era had already acknowledged Trek as being a fictional franchise -- anyone remember Rose calling the Doctor "Mr Spock" in The Empty Child?
Before anyone bashes RTD over this, let's wait and see what he really wrote in his book, first. This is just paraphrasing. RTD was known for brainstorming, but also had the good sense to veto many of these ideas - such as Rose Tyler: Earth Defense.
Enterprise was cancelled months before Doctor Who returned to DVD, and I can't see RTD doing anything with Trek in that first year back, so if the idea ever existed, it likely died a-borning.
I do wish RTD had kept a line of Steven Moffat's though. When Rose calls him "Mr Spock" the Doctor was originally to have replied "I'd rather be 'Doctor Who' than 'Star Trek'" !