I have a road bike with front suspension. In May, I'm doing a charity bike ride through the some mountain terrain and I've heard from others that a front suspension adds significantly to mechanical drag when climbing hills. Unfortunately, I can't lock out my front suspension, nor is it practical for me to find a another road bike to use on this ride.
I've thought about switching out the front fork for times I do rides with these types of climbs, but I'm not sure how much that would cost.

If it's for charity, then just ride.

What is your bike???

What kind of road bike has a suspension fork?
If you are a decent rider and doing a fair amount of climbing which includes a lot of out the saddle, than bobbing is going to be a real problem...not only for control but as a power robber as you alluded.
On my 29er I have a Reba Race 100mm travel shock with a lock out that is just a fantastic fork. If I couldn't lock it out when needed it wouldn't be much fun however. If you plan on keeping the bike after the ride, you want a fork you can lock out if you must have a suspension fork.
Good Luck.

I'm not trying to win any race. I just want to finish. And while I'm training for the challenging hills, I did this ride last year and the hills were torture for me. So I want to know how things such as a suspension front fork work againsts mechanical efficiency when climbing hills - especially when other riders pointed out this out to me last year. My bike is a Lemond road bike that came free with my friend's Saturn in 2003. I bought the bike from him 2 years ago.

A LeMond road bike with suspension? Pics?

Honestly I don't think it's going to make as much difference as some would have you believe. My road bike is my main ride but I have taken my hybrid out on some hilly long rides and with a suspension fork, upright position and flat bars it's fun and surprisingly comfy and my speed has been just fine. Ride what you have and enjoy it.

Partly the amount of inefficiency depends on your riding style. If you're shifting your weight back and forth with each pedal stroke and therefore compressing the suspension you'll be wasting some energy in the process. But with a smoother style the suspension fork won't really be doing much when ridden on pavement and in that case the effect should be minimal.

One time while on the Solvang Century (before they repaved Foxen Canyon) I was lusting after a Cannondale Silk Road bike when I saw some riders enjoying them.
They only have around 1 inch of travel so I think any power loss would be insignificant.
If you're going to climb hills you have to prepare yourself, regardless of the fork on your bike.