There you are seated on a wooden chair, and before you a wooden table. On top is a white clothed table cover, stainless and without a single wrinkle or crease. In front of you, there is a wooden mug filled with your prized drink on the clothed table. You can drink every bits of liquid there is inside it, but would you want to refill should you empty it or lessen it's contents?
Unless it's a rather large (>2 pint) mug, then yeah, I'd want at least 1 refill of pretty much anything I'd be willing to drink.
When asked if you want a refill, the answer is always yes, provided that the refill is free of charge and obligation. Ai-chan wouldn't want to refill Ai-chan's cup of coffee if it means Ai-chan has to slaughter a whole village. That's just not kosher.
I wouldn't leave b4 I had my fill. So, whether I want a refill would depend on my then capacity/condition.
I would definitely get a refill if it's FOC, especially when I did enjoyed the drink. I would make sure there's washroom nearby so I can easily access it in my need.
Bits of liquid? I don't know what kind of "liquid" comes in pieces, but I sure as hell wouldn't even consider "drinking" it.
Is it free from any rule from the start to the end, with no subtle texts like requiring charges, only to refill up to some amounts, or some living mortal sacrifices? If it is, then yes.
You are one of the few people whose sentences are beautifully structured yet you make some rookie mistakes like not knowing the differences between its and it's. Not trying to be grammar Nazi or anything, I usually ignore such mistakes but in your case, it's like a swordmaster forgot how to perform simple swings.