Exactly what I did, but I turned it permanently into a TT bike. It was a road bike frame that was a little on the small side, which is essentially all a TT frame is.
I used a Bontrager XXX seatpost which you can actually turn round so the offset is forward (only 5mm but better than backwards).
bar height is another issue, particularly with clip-ons, as to get into a good aero position generally needs a low front end – hence the slightly too small road frame helped me here. Most people can’t produce as much power or are very uncomfortable with a very low front end and end up using loads of spacers and a positive rise stem anyway even on full-on TT bikes – therefore the slightly longer headtube and raised position of clip on bars isn’t too much of an issue – especially if you use a low drop stem (eg 17 degree drop).
Another downside to just using clip ons with your road bars/shifters is to change gear you need to take your arm off the clip on bars. With practice this can be done reasonably smoothly, but it’s much slicker on the end of the clips ons!
I’ll try and dig out a picture of my set up.