In principle sure, as long as you use a different polymer with similar biochemical stability, but a lot of money and tech development has gone into reading and synthesizing DNA in particular. Why reinvent the wheel, so to speak.
In fact it might be even better with DNA, since you can use much bigger "alphabet" for this purpose, than nature gave us. Would tremendously increase storage capacity.
...at the cost of bit errors.
There are already xenobases being developed, eg Romesburg. Those add extra bases beyond the 4-5 seen in nature.
I know and was referring to them.
Not just tech... life has already provided us with optimized tools for reading, writing, translating, and correcting DNA. The chemical properties of DNA are well known, and it's an incredibly stable molecule.
Doesnt really make sense to switch to a different copolymer.