In GURPS, double-counting penalties is generally unfair. You can't, say, give someone a -2 to DX and a -1 to defenses, and then apply the -2 to DX to skill to get a -1 to defenses and then give the basic -1 on top of that . . . it's clearly included already.
But I generally feel that broadly applied penalties and bonuses are a good thing. As long as a penalty doesn't penalize the same score twice, it's probably okay.
My reasoning for this is that bonuses work the same way.
Take for example the spell Grace (GURPS Magic, p. 37). Give any random delver a +4 to DX, and said delver gets +1 to Speed, and therefore +1 to Dodge . . . and a +4 to Acrobatics rolls for an Acrobatic Dodge for a +2 to defend. No one would argue that a +4 to DX shouldn't give you, say, a +4 to skill rolls based on DX. Nor does it make much sense to say that +4 DX doesn't increase your Speed, and thus your Dodge. Nevermind the actually wording of the spell says specifically it does this stuff.
Equally, a penalty of -4 to your DX from Clumsiness (p. 36) would give a -1 to Speed, and thus a -1 to defend, and make your chances of pulling off that Acrobatic Dodge go down as you take a -4 to that, too. You'd still get your +2 if you made the roll, but you aren't nearly as likely to succeed.
I'm hard pressed to think of a penalty in GURPS that violates this rule - I couldn't find one flipping around. There are penalties which only affect one thing (Stunning gives a -4 to defenses, but not much else . . . not that you can do other things while stunned), or have specific penalties that don't match the usual calculations (posture penalties, say) . . . but otherwise, if you modify the stat you modify the effects.
This is all a long-winded way of explaining why I don't really think it's double-jeopardy to suffer an Encumbrance-based penalty to a skill that might be used to defend, and which also might need another roll on its own - Acrobatics and Acrobatic Dodge. I'm willing to entertain contrary examples, but ones such as Grace and Clumsiness argue strongly that the way I do it is the way to do things.