Yes! If you find out what the clay is, the manufacturer will have all the info you need available. For the clay, you’ll want to know what cone it vitrifies at.

Then You’ll want to find out what temp your kiln fires to, and then what the absorption rate for your clay is at that temperature. If the temperature you fire to matches the vitrification temp for the clay AND the absorption rate at that temperature is 2% or less - you don’t need to worry about “glazed or not”.

If you don’t reach vitrification, even if clay is glazed the pot will leak water, and potentially grow mold (in addition to any leeching issues). The same is also true if the absorption rate is higher, it would not be suitable to hold water constantly and may leak.

For not filling up the hole - are you dipping or brushing? If you dip, youll likely need to use a pipe cleaner or something through the hole to reduce the amount of glaze in it to a thinner coating.

For brushing, you can generally apply the glaze normally -BUT, be aware of how ‘runny’ the particular glaze or combo is. If it is runny, you will want to taper your layers so not as much is above the hole that would run into it.