No. As a general rule, while on the job, military personnel are required to wear uniforms and the combat uniform, the service uniform (Dress Blues in the Navy), and the Mess Uniform (Dress White in the Navy). Combat Uniforms are work casual and are your standard camo uniforms (except the Coast Guard's which are solid blue) and typically given a different pattern for different branches (Army, Marines, and Airforce all have different camo patterns with various shades of green. Navy has a blue camo pattern, Coast Guard has solid blue uniform). According to a military buddy, these are actually pretty comfortable to wear.
Service Uniforms are the military equivalent of formal office wear and would be worn anytime a male civilian would be expected to wear a suit and tie (court martial, meetings with politicians or VIPs including Congressional testimony, press conferences). The Mess uniform is for formal events, such as service balls and galas, promotion ceremonies, change of command ceremonies, weddings (traditionally, especially in the Navy and Marines, though I'm fuzzy if it's a rule or just a de facto thing).
As a rule, you are expected to be in proper uniform while performing your duties unless a few exceptions. For example, rank isn't worn in forward operating bases (for the same reason Lt. Dan told Forest and Bubba to not salute him when they first meet) or if you are a guard of the Tomb of the Unknown Soldier (because no one is allowed to outrank the Unknown Solider... save for George Washington, who is by law the highest ranked person in the United States military for all time). Additionally since the Navy provides many of the non-combat service roles for the Marines (JAG, Doctors, Chaplains), Navy personnel assigned to Marine units will wear marine combat uniforms while embedded with the unit.
It is possible for military personnel to be given orders to dress like civilians. Generally this means that they are being ordered to go somewhere and/or do something that the military officially doesn't want to be associated with doing or going to. This is usually done when it's in the best interest to avoid the the implication of people who clearly work with the military being there for whatever reason. And it's avoided unless absolutely necessary (if captured, being in a clearly identifiable uniform is one of the four requirements for Geneva convention protections for Prisoners of War. This is important as you're not allowed to torture or kill POWs once they surrender (and you can't shoot them if they escape a POW camp and later surrender again... Only while they are still resisting by running away). With out a uniform, you don't qualify and you go to the enemy nation's criminal justice system. Hope they have respect for due process and human rights... though most enemy nations of the U.S. aren't all that great in almost all historical contexts.). So while these orders are rarely issued, they can be... and they are sometimes more serious than your bog standard "casual Fridays."
Oh, and you're not really supposed to consider Congress as an enemy*, considering they pay for all your cool toys... and a lot of prohibited practices in the Geneva Conventions are perfectly legal for a nation to use on it's own personnel (you can not use tear gas enemy soldiers. But you can gas your own troops all you want as far as War Crime tribunals are concerned. That said, as bad as it sounds, being grilled by that idiot in congress, [Insert name of preferred congressional idiot here], for five minutes is not a violation of Geneva Conventions on use of torture.
According to DOD policy, the proper term for a hostile force is "adversary" not "enemy". The U.S. Army's greatest and only enemy in every war is the U.S. Navy. (It's a bit of inter-service rivalry humor and if you ask any member of any branch, they are more than willing to rescue a member of another branch... they will also be officially grateful to another branch saving their bacon... unofficially, they will bitch about being saved by worst service in the military the whole way back to the safe zone.)