I have always heavily RP'd all of my characters in TES. ESo will be no different. I was worried about being to initiate my same RP tactics in ESO and I begged the question if it was possible. After participating in several betas, the answer to that is a profound yes.
My core efforts to RPing is summed up as.. " If it's not fitting for the character's personality, then don't do it."
RPing, to me is not about drinking, eating, sleeping... those are immersion aspects. RP is about the personality of the character and allowing every action and choice be governed by that. This holds true to ESO.
The chat channel is not an issue for me, because I disable that stupid thing. It takes up precious real estate on my HUD. Real Estate that I prefer to be vacant. If someone wants to talk to my character, they have other options. I am not well versed in the application and effectiveness of the different 3rd party audio softwares but I'm wanting to give them a try.
When my character is in the gameworld, they don't see other players. Everyone is just another NPC. The idiots running around and jumping frantically everywhere are written off as a crazed skooma addict and virtually ignored. It is a little bit of getting used to a bunch of others doing the same thing but I basically ignore them as well.
The thing that I am excited about is actually talking for my character. It places me into more of a role where I'm playing as the character. My norm is viewing the character as their own entity and I'm just a spiritual guide following along behind them.