Well, you could.
I would suggest getting some lighter fluid though.
A couple of problems I can foresee:
1) alcohol is more volatile than the somewhat heavy fuel used in lighter fluid, and is somewhat more likely to flash. This probably isn't too big an issue.
2) alcohol probably has about half the energy per unit volume as lighter fluid and does not burn as hot.
3) The water and alcohol will soak into the charcoal. The alcohol will burn and the water will stay, and to some degree keep the charcoal cool by evaperation.
I expect it is possible to use, but probably isn't as safe (but not too bad), and will definitely do a much poorer job at getting it lit.
Got a (large) coffee can, some wire coat hanger, and old newspaper? You can make a lighter that will work great and not use any volatile fuel at all. It may work so well, you will never go back.
1) Cut both ends out of the coffee can.
2) Punch holes through the side of the coffee can near the center vertically.
3) Put pieces of coat hanger through from one side of the can to the other.
4) The point of 2 and 3 and to make a "shelf" of coat hanger wire about mid way up the can that will allow you to fill the top half with charcoal.
To use, fill the bottom with wadded up balls of newspaper, fill the top with charcoal. Place the full can on food grate if necessary, hopefully the grill has a lower charcoal grate. Anyway, the can needs free air flow from the bottom, don't place it on a flat solid surface. Light paper. Wait a few minutes.
If you bought a fancy charcoal starter like this, you would now appreciate that it has a handle on the side so that you can dump out the now perfect coals without burning your hands. You will need oven mitts or something to dump the can into the bottom of the grill.
Once the paper get the coals burning at all, the heat will keep air flowing up throw the can like a chimney and really get the coals lit well, in just a few minutes.