Yes and no. Anything that absorbs a liquid that is not clear will also absorb the liquid's color, so yes. If you were to use a pH strip to absorb a wort solution that is high in the SRM scale, it will also absorb that wort's color as well.
With that said, the amount of solution it is absorbing pales in comparison (hardy-har-har) to what you would pour in a pint glass, therefor it is significantly more translucent, and therefor not as dark in appearance. A simple way to demonstrate this is to take your pint glass with a stout in it, and dipping a paper towel in it, versus dipping your pH strip. The pH strip absorbs less, therefor it is more translucent, allowing more light to pass through, allowing you to get a more accurate reading. That's in part why the litmus paper is so thin, so that the minimal amount of liquid it can absorb won't obscure the results too much.
All that said, the margin of error (and interpretation) for pH strips makes this issue negligible at best. Litmus paper becomes more and more unreliable with time since their accuracy degrades the longer they're exposed to oxygen and humidity. So long as you use pH strips specific to homebrewing, you should be able to get within an acceptably accurate range. If you're looking for absolute precision, you'll have to go with a digital pH meter.