Yes, SSL is fully supported. Your website and your scripts can operate in SSL mode (Curl SSL is also enabled for PHP).
Currently only 'Gold' shared hosting plan and both reseller hosting plans support SSL certificates. To add, if you have any troubles installing the certificate on such an account, please let us know and we will install it for you. We can install either self-generated or Your private SSL. Please mind that we do not have private SSL certificates on offer and they need to be purchased separately and installed on the account later on.