Most indubitably. Just as if you cut off your leg, you can't break that leg. Most people who say they don't have any personal information stored in their phones don't realize how much they actually DO have stored in their phones. They have all their friends' phone numbers and possibly their addresses and most likely they have those friends' email addresses. Often, that is all the hackers are after.
The good news is that a dumb phone can't load apps that will access things outside of their own self-contained, programed functions. Nor can a "virus" or Trojan horse App be side-loaded on such a phone from a spurious source other than by the carrier's own store. That makes them absolutely safe. The BlueBorne's danger was that it apparently could use the small amount of memory in the Bluetooth's dedicated circuitry to hide a small bit of malicious code, but I sincerely doubt that code could ever be used by a dumb phone to be sent to another device. I am not sure whether another device could download that malicious code FROM that dumb phone, though, as part of the handshaking while connecting. I really doubt it.
All I have is phone numbers.
No email addresses or home addresses.