Fender itself does/did it. The first and second one I came up googlinghttp://www.jimlawrence.net/BASSES/TeleBlonde.html andhttp://www.jimlawrence.net/TELE73BASS/1973TELE.html
have both very untelecasterily (is that even a word?) a horn. In fact, it doesn't look at all like a Tele, but more of a Precision. Probably it was just a marketing thing. ibanez did also copies, but they seem to have been like the Fender ones.
So I suppose there would be problems with neck heaviness using the standard telecaster shape. But perhaps you could try it - just don't make it an extra longscale, hmm? And look for more, I suppose someone must have tried it before.
Oh, don't stone me to death please, but one suggestion I just came up with: you could make it a headless perhaps?