There is no specific hosting requirement from Magento side to use APPSeCONNECT. There are two ways it can be done :
1. Sharing hosting should not make the Magento site slow ( Magento site needs to have more quick load time).
2. APPSeCONNECT needs the Magento admin and FTP credentials so as to install an extension in Magento, and also to call webservices API to fetch data for the integration.