Welcome to TFP.
While a cover may reduce the amount of debris that gets into the pool, I'm going to hazard a guess that your pool service is also managing your water chemistry, in which case the answer is no.
If you're interested in reducing or eliminating the service, purchasing one of the recommended test kits (TFT100 or Taylor 2006, here's a link :
TFTestkits.net) and reading through Pool School would arm you with the knowledge to maintain your own water chemistry in a very easy and quick way daily.
Then you could choose how frequently you have a service come in terms of the "physical" labor such as vacuuming. OT for that atter, purchase a robot cleaner instead.
Let us know if we can assist.
Also note that while covers can reduce debris, conserve heat, and to some extent reduce chemical useage, pool water does benefit from sunlight and open air to reduce combined chloramines, ccs or spent chlorine by products that need to be broken down. So you would not want to leave the cover on all the time.