It's all important; a dedicated line can still bring all the bad results that are present on the line to your gear. I was advised a long time ago that you had to look at power as an entire component of your system from the point the main power lead comes close to your house all the way into your system. That's why you'll see people, even those of us with power conditioners, tackling power from the meter (and before) all the way to the speaker so to speak. Here are the areas I have focused on; please note that at various points people suggested isolation transformers to me as well but it seemed that for every positive vote, I'd collect one or two negative votes against the idea for various reasons including some curtailing dynamic headroom and current, those that injected noise into the room, house or line, etc....so I've not gone down that route.
Here are the main areas I've chosen to focus on;
Grounding: Dual 1" diameter 10' ground rods pounded in 8' apart outside the house; 4 gauge solid copper ground leads attached in series to from ground rod-1 to rod-2 to the meter-head going into house; CADWELD bonding of ground wires to rods and to meter head instead of clips which can expand, contract and loosen, corrode, etc...
More Grounding: Environmental Potentials EP-2750 Ground Filters on feed from main panel to sub-panel and on my dedicated circuit(s) in the sub-panel...
More More Grounding
cool
: Granite Audio Ground Zero star-grounding system to everything (except speakers)
Power and Ground Quality: Cutler-Hammer main house panel and GE Sub-panel, both with COPPER BUS BARs
Power Conditioning: Environmental Potentials EP-2050 Wave-Form Correction & Surge Suppression Device (on main house panel)
Isotek EVO3 TITAN for power amp power conditioning
Isotek EVO3 SIGMAS for front-end power conditioning
for further details, see my system posting...
Regardless whether you utilize the products I list above or other alternatives, I'd suggest that in addition to a dedicated line, you put together a plan to attack all the categories above; I did and frankly it's the part of the system that I look at and say 'done' more often than any other...
***On the subject of multiple dedicated circuits feeding the same system; I've been down this road several different ways. It is a good idea but like feeding multiple duplexes off the same dedicated circuit, you have to focus doubly hard to verifying that you have the exact same ground potential on every power outlet or your equipment will not see the same ground plane which will have various ways of manifesting itself in your audio system (ground loops/hum, lack of blackest backgrounds possible, etc....)