Yes, 100% playable offline. Dark Souls (Prepare to Die Edition / Remastered) is fundamentally a single-player experience.
Offline is harder—no summons for bosses (Ornstein & Smough, Four Kings, Gwyn). But many consider it the purest experience. NPC summons (Solaire, Lautrec, Beatrice, Witch Beatrice) still work offline.
Recommendation: Play offline first. Go online for co-op/PvP on NG+.