Can you save tables with Data Store?

According to the documentation on Data store, yes you can.

Saves arbitrary lua tables, besides strings, booleans and numbers. Instances cannot be saved directly though.

However, it should be noted that there is an odd limitation related to storing tables in Data store.

You cannot use a mixed list style (which is essentially where you are using both array and dictionary table styles in the same table). An example of this would be the table below...

local t = {1, b = 2} -- note how the first raw element "1" is in array style, while the second raw element "b = 2" is in dictionary style.