In the context of the original question, "no" - a casino can not prove, or in any way act upon, your luck. Implicit in the premise is that if it is possible to happen, it is obliged to - so long as it deems successful. Given that that you want to succeed in obtaining windfall gambling profits, nothing can inhibit that - including the casino actively taking a role against your success. You will be, in fact, cheating (by definition), but it doesn't matter - the setup provided disallows the casino from doing anything to inhibit your success - at least for that day.
"Anything I do throughout this day will yield a successful outcome, no matter what the odds against it are, but only if it's possible to happen in a day."
I think it's important to consider your luck in a larger context. Your luck isn't bound to the casino, it applies to every single thing you do that day.
In ways you wouldn't even consciously "wish" - things would simply work in your favor, from security not being able to adequately monitor you, to thieves deciding not to mug you, to the In-N-Out behind the Monte Carlo not giving you dysentery.
Perhaps upon entering the casino, you are told that you are the millionth guest, and have won the entire casino or its contents - your choice. Maybe you simply win every bet you make, and against all reason, are invited to every other casino on the strip to win there as well.
Why even stop off in Vegas?
You only have to set a goal that is possible, however improbable. Finding winning Powerball tickets in the gutter, or 100 of them isn't impossible, only improbable.
Of course thinking of it in this context really blows the doors open, and drifts further away from your original question, so I'll refrain from further exploration. Needless to say, there are infinite outcomes that aren't impossible that would probably yield better results than the finite funds in a casino (a real estate tycoon uncle you didn't know you had leaves you his empire, etc.)