No it is not possible.
Those headers are not included in the server IMAP response in any way.
You can try requesting specific e-mail headers:
List<MessageData> list = client.GetSpecificHeadersByUID(
uids,
new[] {"IMPORTANCE"});
IMail email = new MailBuilder().CreateFromEml(list[0].EmlData);
var importance = email.Importance;
...however it won't be as fast as GetMessageInfoByUID().
Alternatively you can search for messages with specific header value:
List<long> uids = client.Search(
Expression.Header("Importance", "High"));