The bolt should close freely. If I am setting up a target rifle, I will cut the chamber so that I can just feel the GO gauge, to insure minimum standard headspace. If the gauge can be felt firmly - never force the bolt closed on a gauge - headspace may be too tight to allow standard cartridges to be easily chambered. If the rifle is an autoloader (like M305, etc.), the bolt MUST close freely on the gauge - there is a risk of slamfires otherwise.
NO GO - With the bolt stripped, you should be able to feel the gauge when closing the bolt very gently, before the bolt fully locks. It very well might be possible to push the bolt to full locked position, but that does not give a correct reading.
Use a light touch with gauges.