Can Trello be set up to automatically send emails from certain email addresses directly to client's card?
You could accomplish this with a combination of Trello's card-specific emails and email filtering/forwarding or IFTTT.
First, grab the email address for the card you want to add comments to. You'll find this under "Share and More" on the back of the card.
Depending on your email provider, there are various ways to forward emails based on a rule or filter. Basically, you want to look for all emails from those certain addresses and forward them to the card's email address.
If you're using Gmail, here's an example using IFTTT:
If you're using Outlook/Exchange, here's an example using inbox rules:
It's the same concept, just two different ways of implementing it.