Yes. Spells are unaffected by Apparition.
Whilst he didn't perform the spell on himself, Ron did have his appearance altered magically before his trip to Gringotts.
Hermione sighed and set to work, muttering under her breath as she transformed various aspects of Ron’s appearance. He was to be given a completely fake identity, and they were trusting to the malevolent aura cast by Bellatrix to protect him.
(Deathly Hallows, Chapter 26, Gringotts).
After he Apparates his disguise is still intact.
Harry turned on the spot, with Griphook on his shoulders, concentrating with all his might on the Leaky Cauldron, the inn that was the entrance to Diagon Alley. The goblin clung even tighter as they moved into the compressing darkness, and seconds later Harry’s feet found pavement and he opened his eyes on Charing Cross Road.
[...]
Travers seemed a little taken aback at that, and he turned instead to Ron.
“Who is your friend? I do not recognize him.”
(Deathly Hallows, Chapter 26, Gringotts).
The most natural conclusion is that spells are unaffected by Apparition.