Yeah you can play solely with the keyboard definitely. You have the option of customizing all the keyboard key bindings to what you want. The only thing that I imagine will cause issues is camera movement and targeting.
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I have been playing on PC with a PS3 controller and the only problems I have had are related to my own forgetfulness, like forgetting to switch back to my combat cross hotbar from my pre-fight buff cross hotbar. Therein lies the problem, there are limited slots on the cross hotbar as compared to the regular hotbar. Throw in trying to micromanage a pet and now you have even more hotbar slot issues.
That said, I have always been primarily a console gamer and I'm just more comfortable with a controller in my hand. I don't think learning to manage multiple hotbars is going to make me switch to K/M gaming.
I switched off weapon drawn/sheathed filter options, set the L1+[Square][Cross][Circle][Triangle] filters to Enemies, Attacking Enemies, Friends & All.
I use a Sony Dual-Shock clip-on keyboard which I've key-mapped the numeric keys to numbered party members for instant targeting of the first 8 party members & pet.
As a last resort L1+RStick switches the PS3 to mouse mode if I feel the need to instant select anything with the left analogue stick.
I had to switch direct chat off otherwise any keyboard presses go straight to the chat window and not to your mapping. I also needed to change some of the default keyboard mapping to use shift instead of Ctrl/Alt as the PS3 clip-on keyboard doesn't have those keys.
I've not had much trouble healing quickly so far with this set-up.