Absolutely correct. On both accounts- tipping is always appreciated, and when you do well &/or up front, it pays dividends.
I have had offers which included Drinks on Us in the Casino (only) and Elite offers which included Drinks On Us- Everywhere. I have never been charged anything (exactly $0.00) with the Drinks On Us- either type.
EXCEPT when sailing from Galveston where you pay sales tax for TX, which ended up being 67¢ or so for a drink-- and cannot start using either of the drink packages the first day- but you also don't pay for the first day of Cheers! (Same in NY from what I see, but never sailed from there.)
Which was genuinely surprising, because I thought it was essentially the same as Cheers! (It is in so many if not all other ways.)
But of course I tip well.
And the first time I was there, I didn't even know I was going to get free drinks later in the evening, but they said based my casino points... obviously very nice.