Contact While Taking a Penalty Turn

No, because the requirement to stay clear during turns is not a part 2 ("when boats meet") rule, it is a part 4 rule (44.2). 44.1 allows turns as a penalty for part 2 violations only.

Similarly, you can't pump and then exonerate yourself by turns, because the "means of propulsion" rules are in part 4, not part 2. 

Easiest to start with the rules themselves:

A boat that may have broken a rule of Part 2 while racing may take a penalty at the time of the incident. Her penalty shall be a Two-Turns Penalty unless the sailing instructions specify the use of the Scoring Penalty or some other penalty. However, if she caused injury or serious damage or gained a significant advantage in the race or series by her breach her penalty shall be to retire.

After getting well clear of other boats as soon after the incident as possible, a boat takes a Two-Turns Penalty by promptly making two turns in the same direction, including two tacks and two gybes. When a boat takes the penalty at or near the finishing line, she shall sail completely to the course side of the line before finishing.

Separately:

20 STARTING ERRORS; PENALTY TURNS; MOVING  ASTERN

20.2 A boat making a penalty turn shall keep clear of one that is not.

So, the requirement of a boat doing a penalty turn to keep clear is not part of rule 44, but is part of rule 20. (However, the requirement to get well clear is part of 44 - but "get well clear" isn't actually defined). Rule 20 is in part 2, so  if you hit someone while taking a two turn penalty, you have infringed a rule of part 2, and should exonerate yourself by taking another two turn penalty (Unless, of course, you have caused serious damage, or injury, or gained a a signifcant advantage.)

Also: