In normal times, yes, you could just turn up and he could enter as a visitor and you could sponsor him later. There is something called "dual intent" which is a visitor intending comply with visitor regulations provided he is not successfully sponsored. However, getting sponsored is not a sufficient (or even good) reason to enter the country normally. So it's a delicate tightrope: under normal circumstances your husband would need a reason to travel to Canada with you that isn't getting sponsored - for example you're visiting your brother.
I'm sorry to say I don't have any idea how this is all being enforced right now. As a citizen, you have the right to enter the country. As your spouse, your husband has the right to accompany you as an exception to the travel restrictions (I believe). But if the border guard believes you're trying to immigrate, this could pose a problem. (It would normally but especially now, I suspect.)
And it's important to remember that he cannot lie. Lying is an offense under the immigration act and can result in revoked status for your husband. (Though how often this happens to Americans...)
One other thing to keep in mind: if you want to sponsor him while he's still in the US, it's not good for you to be in the US too. You would then need to prove your intent to settle here (owning property, jobs/job offers, etc.).