When the 3rd-party agrees to follow the OGL 1.0a
Clause 3 states:
Offer and Acceptance: By Using the Open Game Content You indicate Your acceptance of the terms of this License.
And clause 10 says:
Copy of this License: You MUST include a copy of this License with every copy of the Open Game Content You Distribute.
So, if you use Open Game Content and include a copy of the licence (or other indication of your intent to be bound) then you are bound by the OGL 1.0a.
If you use Open Game Content under fair use/dealing, or illegally, then you are not bound.
How much of the Open Game Content is protected by copyright?
Game rules are a procedure and procedures are not protected by copyright. However, the particular presentation of those rules by Wizards of the Coast (WotC) is protected by copyright as are any components that are not rules. AFAIK there is no case law on Dungeons & Dragons on where this line is drawn.
If your “derivative” work draws only on the rules, then there is no copyright infringement. However, even if it draws on things that are protected by copyright, you might have a fair use defence in the US but you are unlikely to have a fair dealing defence in Commonwealth nations. I can’t help you with civil law jurisdictions.
There appears to be a general consensus that most of what the Open Game Content contains is stuff that WotC could not successfully prosecute you for using under copyright or trade mark law. Effectively its a licence to allow you to use what you could use anyway - the only thing you gain is the certainty that WotC won’t sue you irrespective of if that suit might be successful.
To put it another way, so long as a creator of such content doesn't quote the SRD content provided as part of their work, nor use any of Wizard of the Coast's trademarked names, nor the rules of the game, would the creator have to comply with the OGL?
As stated above, you can quote a lot of the content, just not the stuff that isn’t rules. You can refer to WotC trade marks in a nominative way, just not in a way that suggests that your product is their product. You can quote all the rules of the game if you like.
That does’t mean that WotC won’t sue you, it just means they will be unlikely to succeed.
If they used the style WoTC (as set out in the style guide made available by Wizards of the Coast on the dmsguild), and applied it to their original works, would that work now fall under the aegis (or dominion) of the OGL?
Following a style guide does not infringe anyone’s copyright. You would need to observe the rights that anyone held in fonts and you could not use the style in an attempt to pass your work off as theirs - style can be a form of trade dress which is a type of trademark.
Is there a test set out to determine if a work is a derivative work (and thus would be covered by the OGL)?
Yes, there most certainly are tests and they vary from country to country. However, as stated above being derivative and following the OGL are two seperate things.