Is the square system compatible with a different card reader

[SLM1822]

My business currently uses a different company's card reader/transaction system but we use a super old-fashioned cash register "system". I'm wondering if we can continue to use our current company's card reader and use Square to essentially track inventory, calculate totals for customers purchases, generate sales receipts and all of the other handy things Square offers - just without using the actual Square card reader.

[LocavoreStore]

We've been doing this for years. We have a separate Merchant account through a local company, so all of our card transactions actually go through a separate physical terminal. We don't usually process many card transactions through Square... Invoices that people pay online end up being processed by Square, but physical sales all go in as "other" tender... 

Sometimes I feel bad for not actually paying much (if anything) to use the software... If you ask me, it's more valuable than the merchant processing. 

[LocavoreStore]

Originally the separate merchant processor was only to handle EBT/Food Stamps transactions. It only made sense to use it for all card transactions.