Will running a double monitor in clamshell mode put more stress on my computer?
Not sure how to answer this objectively, but running it in "clamshell mode" is fine. I've been doing the same for a long time with my MacBook Pro with no issues.

If your external screen is bigger (resolution-wise) than your laptop's native screen, then it will of course need some more graphics power to run, but this is rarely an issue in practice.