Hi David and welcome to the forum,
If email contact is their only means of initial contact, then that is of course your only option. That said, I was personally request phone numbers for any suppliers I was going to do business with. If they weren't prepared to provide a customer service number for me to call, then I wouldn't personally do business with them.
No this is just me of course, however I would want to know that if any problem should arise that I would have a means of getting some attention brought to it straight away and not have to just wait for an email to be answered. As I say, that's just me, but I think it's important to have an instant communication option when you need it, especially in regards to dropshipping.