From the Scottish Football Association rules on Club Licensing (specifically Part 3, Section 03 – The Club as Licence Applicant and the UEFA Licence). Emphasis ours.
"3.1.1 The Licence Applicant may only be a football club, that is the legal entity fully responsible for the football team participating in national and international competitions and which is the legal entity member of the Scottish Football Association (Full or Associate Member). The licence applicant is responsible for the fulfillment of the club licensing criteria. This membership must have been in place at the start of the licence season for a minimum period of three consecutive years.
3.3.1 UEFA Licence Awards for Scottish Premier League Clubs (SPL)
A Licence cannot be transferred from one legal entity to another."
"National Club Licensing applies to Scottish FA member clubs and UEFA Club Licensing applies to Scottish Premier League clubs."
In other words, to play in the SPL you must have a UEFA Club Licence, regardless of whether you actually compete in UEFA competitions or not. (SFL clubs, who in normal circumstances wouldn't be expected to qualify for European tournaments, are dealt with separately via an "extraordinary procedure" in the event that they do.)
So, should Rangers FC be subject to liquidation and then reborn as a "newco", the new company would NOT be eligible for the licence required to play in the SPL, for at least three years. Furthermore, it is plainly and explicitly forbidden under SFA rules for such a licence to be transferred from one legal entity (Rangers FC) to another (New Rangers FC 2012). Well, that's that all sorted out, then. As you were.
[Edited for clarity and latest versions of documentation, 13-4-2012]
[EDIT 17-4-2012: We rang the SFA yesterday, and they confirmed our interpretation of the rules above. Half an hour later they rang us back, sounding very nervous, and changed their line, stating that the UEFA Club Licence DID only apply to UEFA competitions, and only a National Club Licence was required to play in the SPL. Later that evening it was revealed that the Association is considering disbanding the SPL and SFL entirely and replacing them with a new National Football League. The SFA did not comment on the possible position of a newco Rangers in such a league.]