So my question is in regards to the new "You are a Sympathetic Cylon" card from Pegasus, not the original "You are a Sympathizer" card from the base game.

You get to infilitrate Galactica when you are a Sympathetic Cylon. Per the rules on infiltration, page 11 of the Pegasus rule book, you are treated as a human player with the noted exceptions. So here's my question in the form of an example:

I'm playing Helo. I get the Sympathetic Cylon card in the sleeper phase. I go back to Galactica and infiltrate. Since I'm treated as a human player again, do my character abilities and disadvantages come back into play until I stop infiltrating?

No. Just like the original sympathizer, you immediately lose all your character abilities, flip your card over and move to the resurrection ship. When you infiltrate you are no longer Helo, just sympathetic cylon #7. No skill set, no weakness, no per turn or OPG abilities.