I'm mid-way through a Soul Level 1 playthrough, using the Pyromancer class of course (since it's the only class that starts at SL1).
The only rules I've chosen for the playthrough is that I'm not allowed to increase my Soul Level, and I'm not allowed to summon human players. Upgrading weapons, armour, shield, pyromancy flame are all okay, plus I've also learned a few sorceries and miracles. I am limited in my choice of items however, since I can't upgrade my stats to meet the requirements of many of them (eg. I can't use the Drake Sword or any type of spear), and I only have 2 slots for magic/pyromancy spells. Summoning NPCs is okay.
The last couple of times I played using this character I defeated the Bell Gargoyles, the Capra Demon and the Gaping Dragon. I'm currently somewhere in the middle of Blighttown.
I wouldn't say I'm having any more difficulty with the game than I did on my first regular playthrough. I should be able to finish the game eventually.
UPDATE: I've now completed Anor Londo, obtaining the Lordvessel, and have also defeated the Four Kings boss. Ornstein & Smough presented quite a challenge, but I figured them out in the end!