Can attachments to Salesforce records be attached using the Apex Data Loader?

Answer: See the explanation.

Explanation:
The csv file would need to have these columns:
ParentId – the Salesforce ID of the parent record to which the attachment should be attached. For example, Account record ID 0019000000CZYfN
Name – The name with which this attachment should be saved in SFDC
(We can give any name, not necessary it should be the file name)
File Attachment1 IsPrivate
0 if the attachment is not private; 1 if it is private. OwnerId