It shouldn't be that much bigger of a job. All you need is to get a new stem to match your new handlebars. If you're already replacing the handlebars, the incremental amount of work required to also replace the stem is close to zero (it's basically two extra bolts to deal with). Most of the work will be involved in moving all the control levers and grips over to the new bars. You'll probably spend more time researching which stem to get than actually installing it. Unless of course the bike has an oddball steerer diameter to match the oddball handlebar diameter.

The only thing that might cause headaches is if you're trying to change the fit of the bike by raising or lowering the bars, in which case you may need to mess around with stem spacers (not a big deal) or even cut down the steerer (here's where it starts getting more involved).