Short answer is Yes. Keeping it clean can save you money on your utility bill. If your system is already clean, will cleaning it save you additional money? No
If your system has not been serviced in a while and it appears dirty, then there is a good chance that having it professionally cleaned will improve your efficiency and lower your electric bill.
There are more benefits to add here, having the system maintained will also reduce the chance for a break down, maintain warranty coverage and extend the life of your HVAC system.