Passive RFID through objects
UHF will theoretically work. The factors that could decrease reading performance are:


The material and thickness of the bag (metal or metallic insertions like aluminium foil will definitely not work).
The number of tags in the bag and their positions (if two or more UHF tags are pressed one to each other one or all of them will not be read). The more the tags the more the chance for two of them interfering.
The material to which they are fixed (dielectric materials such as liquids, metals will dramatically decrease performance)
Reading distance, tag and reader performance.
Interference by dielectric materials between reader antenna and tag (if a human body is placed between tag and antenna or tag is very close to human body - 2 cm - the reading distance will decrease)


The answer to your last question is Yes in about 99.99999% of the time with a controlled environment.