Your last sentence is helplessly loaded because of course nobody can say our welfare system can tolerate infinite ("unlimited") immigrants. Black holes may be the only system/entity that can absorb an unlimited amount of anything, and even that isn't fully settled.
Could we "accept 100,000 or more radical Muslims at once who disagree with our Constitution and/or culture without any major issues?"
Well, what's "radical"? Is "radical" willing to abide by our laws while despising them? Is "radical" a person who ignores our laws? If so, is it someone able to hide that flaunting of the law from the authorities?
You don't ask a readily answerable question. I would point to the fact that America survives despite the fact that Americans kill around 14,000 other Americans every year and commit around 1,400,000 violent crimes against Americans in the same span. Clearly, we can absorb quite a bit of damage without failing. So if your question is existential as it sounds but I ignore the hyperbole of "unlimited", the answer is: yes. But that's also not the important question.
The important question is precisely how much assimilation do/ought we demand and at what rate? We are a nation of immigrants, yes, but we've also historically been terrible to our immigrants. They made it, yes, but only after being put through their paces and then some. (ie, see treatment of Irish immigrants at the beginning of the 20th century).
It bears pointing out that there is nothing approaching a serious movement in favor of "unlimited" immigration; that this is just absurd hyperbole used by some on the right to criticize "the Left" for the opposition of some on the left to things like the muslim ban that isn't a muslim ban, but is a terrorist ban, except that it is aimed at countries from which terrorists who have attacked America have not come, and so forth.
There are a few people who really want open borders in the literal sense, but they aren't all that many. The rest want a sensible immigration policy.
