Hi Jeff
Honestly, I am unsure about it. We just use Elavon API for processing payment, everything else is handled by Elavon itself, so if you want to be sure, better contact Elavon and ask them about it
Technical, with Elavon payment plugin, customers will enter credit card information directly on your site for processing payment, so to be safe, at least your site must have SSL certificate installed
Regards,
Tuan