1) Most road bars have a diameter of 15/16", whereas MTB bars use 7/8", so those shift levers won't fit as is.
2) Shimano road and MTB front derailleurs use different cable pull ratios, so the Tiagra FD may not shift quite right. Shimano has a flat-bar road FD that is designed for flat bar shifters and full-size road chainrings (52, 53T): http://sheldonbrown.com/harris/derailers-front.html#352. If your outer chainring is smaller (up to 48T), you can just use a MTB front derailleur (like Deore or XT) as long as you match the outer ring size and cable pull direction (usually bottom pull on road bikes).
Well, it's for a Long Haul Trucker. The Front chain rings would be 48 max. The std bar is 25.4cm. I would like to use a 25.8 if possible but no big deal there. The cable pull is bottom. So, would it just be a matter of changing out the FD for the correct pull and rerouting the cable? Or is there a way to do this without rerouting the cable?
If you're able to use those shift levers, look for a bottom pull MTB FD meant for a 48T max chainring. Not sure what you mean by rerouting the cable. It will still run down the down tube, but you'll be attaching it to the shifters differently (obviously, because they are different shifters). Edit: I think this FD can be setup as bottom pull or top pull: http://cgi.ebay.com/New-Shimano-Deor...QQcmdZViewItem.
As for the handlebar, there are two important diameters: at the stem clamp (25.4mm, 25.8mm, 26.0mm, or 31.8mm usually) and where the shifters and everything else clamps (7/8"[22.2mm] or 15/16"[23.8mm]).
For the stem clamp, as long as the diameter matches, the stem doesn't care what kind of bars they are. However, like I mentioned in the previous post, those shifters (7/8") will not fit on a road bar (15/16").