First design with EEPROM
Yes it can work. You want to use an EEPROM to encode complex logic. Now if all you want to try out is an AND gate, you will use only about 2 of the over 10 address lines of your EEPROM and only one of the data output lines. That is of course overkill. But it will work.

HOWEVER, WARNING, BEWARE: the AT27C1024 and AT27C4096 are One-time Programmable Read-only Memory, it's a simple PROM, not EPROM, not EEPROM. You only have one shot. This is not good for experimenting at all! Only good for mass production. And not even for many mass produced applications as you couldn't ever field upgrade your logic (firmware flash impossible!). 

Stick to EEPROMs for experimenting.

Better use 28C16, 28C64, 28C256, or 28C512. Sadly they only have 8 bit of output, not 16 bit of the PROMs that you chose.