Can Prism or InStat aquire data from a database using ODBC?

No. Neither Prism nor InStat can access data bases via ODBC. You'll have to copy and paste, or save as text file and import.

The problem is that Prism (and InStat) format data in an unconventional way. Most statistics programs use a format where each row is a case (subject) and each column is a variable. This format is easy to adapt to databases. So it makes lots of sense (and is easy) to have the statistics program access data from a database using ODBC (a standard that connects lots of programs to lots of databases). But Prism and InStat are formatted differently. Different columns usually represent different experimental conditions. Often there are subcolumns for replicates (or SD or SEM). While it would be easy for Prism to access ODBC databases, it wouldn't be clear what values go where. It wouldn't be helpful.

Do note that Prism's scripting language can be used to output a table to a database. You can build a table in a script (by looping over many sheets, or repeating an analysis for simulations), and then export the table in various ways, including ODBC.