I see the draw for the League Cup 1st Round is made tomorrow. I noticed Partick Thistle (now SPL) are to be included in it and I had a look at the format for this season. It's not explicitly been mentioned anywhere, but I can only see that Inverness have a bye to Round 3 - the last 16!!!
The format employed assumes 5 Scottish teams in Europe but there are only 4 this season. They automatically get byes to the last 16.
However, there seems to be a clause that, in the event of there not being 5 European representatives, then the highest placed team from the league (not European qualified) will assume the position of team 5. If I've interpreted it correctly, this would be a nice unexpected boost!
The format is from this link with section 2 being the relevant bit.
http://www.scottishfootballleague.com/football/league-cup/format/