While I cannot say I have hands on experience with the Magician class (other than trying it out for a bit), several recommended builds suggest that what you really want to up, at least in the long run, is MAG.
Of course, this is not what you wanted to know, but I did find this quote from a discussion regarding the possibility of playing a pure magic user (some spoilers if you don't want to know advanced spell names):
Speaking as a pure mage with maxed out
MAG and endgame magic EQ: it's
completely possible.
You will encounter a lot of
difficulties during your first
playthrough. But you can't just
endlessly pump points into MAG,
sometimes you have to deviate. Dont
hesitate putting points into HP or
Endurance (for armor).
At around level 180~, you will see
that the game basically play itself
with Moving Soul Arrows, and
Firestorm.
Generally you want to plan your route based on your class. Each level has different equipment sets lying around for you to pick up. That having been said, I would personally go something like 1-1, 1-2 (1-2 is really quick), 4-1 (so you have access to a good farming spot, plus the regen ring and crescent falchion), 3-1 (there are 2 or 3 armor sets here, and it's not that difficult besides the damn Cthulu heads), then all of 2, the rest of 4, the rest of 3, 5, and then back to 1.
Once you get a little more experience, you're pretty free to go in whatever order you want. The power levels in the stages are all relative (the first section of each stage is weak, second is hard, then there's a boss), so explore a little.
Best Answer
Yes, it is certainly possible.
None of the Trophies for Demon's Souls are based around online features of the game.
PS3Trophies.Org has a list of the trophies and information on how to achieve them which corroborates this.