I have two switches (one controls a fan and one controls a light) in a box with only one feed wire. The normal pigtail split is used for the blacks to the switches and the whites to the light and fan, ground to grounds. I have a timer with a black, red, white and ground that I will use to control the fan. Ground goes to ground, red goes to the fan, black gets connected to the existing blacks, for the white I pigtailed two short white wires with the white feed wire and connected one to the light switch white, and the other to the whites for the the fan and timer white (it works). Now the question Could I have connected the timer white with the whites for feed, the light and the fan or would that have caused a problem, (I thought it would so that is why I split the feed white off with the pigtail)
It's only a question of what fits in the wire nut. When you buy wire nuts they come with a list of all of the different combinations of wires that will fit in them. Your way is fine - a bit of extra work is all.
Hey, I work at an electrical supply house and I would have to go and get a second opinion if you asked me this question. It is definitley an unusual query! I will tell you that I looked at the picture, and I see what you want to do. All dimmers have a transformer in them, so when you turn the knob or slide the switch, it reduces the voltage. Most dimmers are rated for 600 watts or 1000 watts, although you can get more wattage for considerably more money. What you should check into is something that is commercial grade or more heavy duty, the dimmer in that picture is like one you would put in your house. I am not sure that the dimmer will not hurt the smoker to be honest with you, I would have to ask the guys at work, they are brilliant, and they have been doing this for 30 years! What I do know is that you cant replace real hickory with a smoker, but to each his own!
If this is in a home with 240/120 single phase then yes you could split the whites with no problem. Even if not on the same circuit the neutrals are still coming from the same neutral bar. Wire nut size matters not at all if that were the case people would get one big blue wire nut and put all the wires under it. needless to say don't try that.