Jeremy Crawford's published statements about the rules are considered Rules Canon for D&D 5e (except Adventurer's League, where they are not).

During his stint as GM on Acquisitions Incorporated, he is sure to make rulings from time to time. These will be considered 'published' per copyright law by dint of being on the show. Will those rulings be considered 'The Rules' as far as everybody's D&D 5e games are concerned?

No, Rules as Written are the rules as written in the books and the errata only

Jeremy Crawford makes rulings on Sage Advice and Twitter. He does not make rules there.

Official rulings on how to interpret unclear rules are made in Sage Advice.

The "rules" here are RAW and rulings are interpretations of those rules. Crawford is not at any point (or at least shouldn't be) creating a new RAW. Instead he is giving us his ruling (his interpretation) of the rules (as written in the books). By definition a ruling is not a rule, so Crawford's rulings cannot be a Rule as Written. So, whether via Twitter or Sage Advice, or Acquisitions, Inc., his rulings are not considered to be RAW.

His rulings are often a good yardstick for judging how the designers intended the rules to work though ("Rules as Intended" or RAI). From the Adventurers League FAQ:

Sage Advice is a great barometer for ‘rules-as-intended’

In fact, anything he does on Acquisitions Inc. is probably not even considered Sage Advice:

One exception: the game’s lead rules developer, Jeremy Crawford (@JeremyECrawford on Twitter), can make official rulings and does so in [the Sage Advice Compendium] and on Twitter

Since Acquisitions Inc. is neither of the two sources, they probably aren't even considered to be rulings in the way other Sage Advice ruling are.¹

So, nothing outside of the books and errata is considered to be RAW and Jeremy Crawford's rulings are not "Rules Canon" (RAW) for anything.

His DMing is going to focus on intent and fun, not RAW

In an interview about him taking over Acquisition,s Inc. Jeremy Crawford says much the same thing:

One of the things in our early discussions with Penny Arcade that we talked about, that would be fun about me taking the DM’s seat, is that it would be a chance for me as lead rules designer to actually show how many of these rules can be used, and honestly how they’re intended to be used. Now ultimately my intent doesn’t matter; what really matters is what each DM wants, but it is a chance for me to show off some of the tools we’ve provided so that DMs can see there are all sorts of ways [in the rules] for people to have a fun time and not worry about minutiae. Because we put some of these things in the game precisely to make people’s life more easy and more fun.

Jeremy Crawford will be taking this opportunity to show off the rules and how they can be used to enhance fun at the table, but he makes it clear that he wants to show off the intent of the rules. Additionally, I don't think from his above statements that sticking to or making RAW rulings is going to be a priority at his table. It will certainly be interesting to see how he rules, but it is nothing that any other DM has to worry about.

^{1 - Thanks @NautArch}

Probably not

According to the description given in the rules-as-written tag, rules as written refers to the rules as they appear in the text.

Crawford's rulings are, firstly, only rulings. They're official rulings, and are official interpretations of the rules, but are not themselves rules. As per Why do Crawford's tweets seem to be treated on par with the actual rules?:

Whether or not any given Dungeon Master chooses to utilize Sage Advice as a resource for rules adjudication in D&D Adventurers League play is up to that individual DM. Sage Advice is a great barometer for ‘rules-as-intended’, in any case. As always however, the DM remains the final arbiter of how a rule is to be implemented in their game.

Should he make a ruling at the table, that would be spoken, not even written down, and it would be difficult to interpret that as "rules as written". Even so, it would be unreasonable that table rulings made in the heat of the moment would set precedent for all D&D games, although it may influence individual DMs and inform their decisions.

Crawford can even ignore or change rules at his table if he wishes. He may even make mistakes, although of course this is Jeremy Crawford we're talking about, so this is highly unlikely.