Having dimmers on a separate circuit will help some, but there's a good chance you'll still get noise. Here's why:
SCR dimmers work by delaying the turn-on time of the SCR's in the dimmer circuit by a certain amount of EACH CYCLE of the AC power. What this does for dimming, is to decrease the total power available to the lights, so they get dimmer.
What it does to the power itself is another thing entirely - since each half-cycle of the AC power is partly switched off, by the time the SCR switches the part of each half-cycle that is going to be used, the voltage across the SCR is no longer zero, so switching takes place during a part of the cycle where more voltage is available. SCR's switch so fast, that when they DO turn on, there is a very high frequency "spike", or overshoot, in the voltage. Since the switching happens so fast, this spike carries a lot of high frequency energy, clear up into the Radio bandwidth.
Since the interference is now in Radio Frequency bandwidth, it can actually "broadcast" to the wires and circuit boards in audio gear. Since the bursts of RF caused by the dimmer are still at 120 hZ rates (one for each half of the 60 hZ line frequency) you hear a 120 hZ "buzz" in your gear, and finding out which (or how many) units are guilty is a major pain in the ass.
That was an over-simplified explanation, so any of you junior techs out there, please save the flames - I've been an Electronics Tech since 1965, I've worked on Pro Video and audio gear for several years, and currently (pun recognized, but not originally intended) work in Industrial Automation systems, IT systems, and hold two electrical licences.
If you absolutely MUST have dimmers in your studio to be happy, I would get just ONE, higher quality dimmer that fits in the switch box, turn off the breaker to that box, TEST to make SURE it's off, and replace that particular switch with the dimmer.
To try it, set the dimmer about half-way up, take a guitar with single coil pickups, like a Strat or tele, plug in, turn on the amp, and wave the guitar around overhead (near the dimmed lights) with the volume turned up. If the dimmer is bogus, you'll know IMMEDIATELY, in which case you could move it to the dining room for mood lighting, or whatever. If it causes no problems you can hear with ALL your gear on, do the other lights and rejoice...
I hate bullshit so much, that I didn't even try dimmers in my studio. Instead, I installed two different lighting systems on multiple switches. One system uses incandescent track lights with theater gels for different colors/brightnesses, with 4 different circuits so I can turn on just one, any two or three, or all 4 depending on what mood I want. The other system is for working (maintenance, wiring, etc), and consists of flourescents mounted behind all racks, etc - these are ALWAYS turned off when recording, as flourescents and their ballasts tend to also produce hum.
Hope that helped... Steve