This has now been pretty definitively answered "No" by the novels. However, some people question the canon status of the novels.
Some interesting things:
1)The War Chief is shot and collapses near the end of "the War Games". We do not see what happens to him
2)In "Terror of the Autons" the Time Lord tells the Doctor that a Time Lord he has met is on Earth "And is now called the Master". The Doctor fails to recognise his voice on the phone
3)In "The Deadly Assassin" the "13th incarnation" is used for an elder Time Lord, NOT the Master. It is stated that the Master can no longer regenerate. The Master states that he is hanging on to "this life". There is no indication tat he has reached his 13th incarnation, just that he can't regenerate again.
4)Later, the Ainley Master and Davison's Fifth Doctor get into an altercation over the fact that the Doctor still has eight lives, while the Master feels they should be HIS.
5)In "The Five Doctors", the Time Lords say they can offer the Master a new regeneration cycle. But they don't explicitly state "13 more incarnations".
Here's (someone else's) hypothesis: The War Chief in "The War Games" was on his third incarnation. He may have been known by other names before. He recognises The Second Doctor. The War Lord and his men are armed with Time Lord technology. When they shoot him, he collapses, and is unable to properly regenerate. When The Time Lords arrive, they are able to save him, but the combination of the weaponry, and the long period means his ability to regenerate is lost. Thus The (Delgado) Master is the 4th(and last) incarnation. He vows revenge on the Doctor. At some point he is badly burned/exposed to radiation/whatever, but manages to cling on to life(as played by Pratt and Beevers). Using the power of the Keeper, he transfers his essence into Tremas. Since Tremas is now The master, the Trakenite DNA is rewritten. Thus this is his fifth incarnation, just like the Doctor shortly afterwards. He believes that he should still have eight more lives. The Time Lords offer to restore his eight remaining lives. The Gordon Tipple cameo is the same Tremas/Fifth incarnation. After the Tremas body is destroyed his Time Lord essence still remains, and is able to take over Bruce's body, the same as it did to Tremas. Thus Bruce is incarnation 6. It is unclear whether the Time Lords restored the remainder of his cycle or this is more just clinging to life. The Master still feels the Doctor's remaining lives should be his, so probably the latter. Bruce is sucked into the Eye. The Time Lords ultimately DO restore the Master and thus Yana is the seventh incarnation, Harold Saxon is the eighth.....FASA's "the Doctor Who Role Playing Game" identified the War Chief, the Monk and the Master as different incarnations of the same renegade Time Lord. However in the module "Legions of Death" he appears as a Renegade Time Lord who has been a former ally of the Master. In addition, the non-canon novel "Time's Champion" indicates that the War Chief is in fact an early incarnation of the Master. Canon comics and original novels have since contradicted this.
The Target novel of "Terror of the Autons" (ironically written by Terrance Dicks) indicates they are one and the same...