Is there a way to have email replies to messages sent by script attach itself to the record as it does when I send the message through the NetSuite UI?

This requires Setup > Company > Enable Features > Marketing tab > Capture email replies to be enabled.

Additionally, the reply will only be captured if you are using the internal id of the entity recipient in nlapiSendEmail. It will not work if using a string value for the recipient email.

For example:

nlapiSendEmail( -5, 1234, 'subject', 'email body' , null, null,records ); //This will work

nlapiSendEmail( -5, 'customer@netsuite.com', 'subject', 'email body' , null, null,records ); //This will not work

The internal Id is required in order for the encoded reply to email address to generate.