The short answer is, you should because short sale lenders may not cover utilities and foreclosure does not eliminate these bills.
Some municipalities require that water is paid before you can close. Therefore, if you stay current with payments on the water, you meet this requirement. However, if you are not current on water, there is a chance that the short sale bank or even the buyer of your short sale will pay for your water bill in full, in part, or not at all. If that is the case, you will be responsible for any outstanding balances before you are able to close.
On the other hand, closings do not require that gas or electric is paid in full in order to close. What does that mean to you? You should stay current. A short sale closing or foreclosure will not pay for anything that you owe for gas and electric. Rather than paying a huge lump sum or going to collections with wage garnishments, try to stay current.
Also, most buyers will want to walk through the property with a home inspector while utilities are on. It is usually difficult to have utilities turned on temporarily to have this done. If you are current, a buyer will be able to do this and confirm that they are okay with the home quickly.
Avoid collections or paying a large sum on utilities and close on your short sale with no hiccups. You will avoid huge credit damage and personal liability that foreclosure brings by doing so.