Is there a way to mass convert leads in salesforce into accounts and contacts using a data loader?

  A very reliable although not cheap option is 'ZaapIT' to mass convert leads in salesforce, but it's going to be around $700 a year as you need the 'premium' version and they sell a minimum of 2 user licences.

A cheaper option although only compatible with Lightning environments is 'Multiple Lead Converter'. Another option is 'Bulk Object Field Creator' which is cheap and does seem to work in both classic and lightning environments.