Yes and No.
You can obviously extend the existing half hourly service but assuming the Hawick extension would not be fully double track, adding a further opportunity for single track clashes, 3-5 stations and the current political pressure on skip stopping and part cancellations you'd probably want to increase reliability on the existing line if you were extending it further.
To be honest I'm not sure that extending the dynamic loops will be that helpful, I'd certainly concentrate any spend on the eastern approaches at Waverley, redoubling Calton North Tunnel, 4 tracks through Abbeyhill, double lead at Portobello junction and a full double track alignment from Portobello to Shawfair with new platforms at Brunstane and Newcraighall.
Then you might want to speed up the Borders services to improve Hawick - Edinburgh journey times. A 2tph stopping service to a new 3 platform station at Redheugh would be my preferred way of achieving this.
You'd then have a 2tph semi fast calling at:
Hawick, Newtown St Boswells, Melrose East / BGH, Tweedbank, Galashiels, Stow, Gorebridge, Eskbank, Newcraighall
and a 2tph stopper calling at:
Redheugh, Newtongrange, Eskbank, Shawfair, Newcraighall, Brunstane, Abbeyhill
That gives you a 4tph service at the two most prominent stations Eskbank and Newcraighall while also improving reliability and journey times.