Yes, one of the good things about Greasemonkey is that it can run scripts on a page, even if javascript is disabled for that page. And, no, it does not unblock the page's JS.
Unless you use Script Injection, Greasemonkey scripts always operate in a separate scope -- which is not switched off by NoScript, etc.
Additionally, GM scripts will operate from a sandbox depending on the effective @grant
settings. See "Why is window (and unsafeWindow) not the same from a userscript as from a tag?" for more information.