No.
Logopolis
The episode is called Logopolis and is also the first appearance of Peter Davison (the fifth Doctor).
The Fifth Doctor debuted at the end of the episode 'Logopolis' and his first proper episode was 'Castrovalva.'
The last episode which featured Tom Baker as a regular was Part 4 of Logopolis.
If you're talking about Tom Baker from Doctor Who, then he's still alive. If you're talking about the fourth doctor, then yeah. In the episode "Logopolis."
Doctor Who - 1963 Logopolis Part Two 18-26 is rated/received certificates of: UK:12 (DVD rating)
Doctor Who - 1963 Logopolis Part Four 18-28 is rated/received certificates of: UK:12 (DVD rating)
Doctor Who - 1963 Logopolis Part One 18-25 is rated/received certificates of: UK:12 (DVD rating)
Doctor Who - 1963 Logopolis Part Three 18-27 is rated/received certificates of: UK:12 (DVD rating)
The 4th Doctor's last story was Logopolis.
Yes, he can. Dr. Who's 4th doctor (Tom Baker) falls from the top of the structure in his last episode ("logopolis") and regenerates into the 5th doctor (Peter Davison) in front of his companions. Additionally, after the 7th doctor (Sylvester McCoy) is accidentally shot in a gang dispute, he is taken to a local hospital where he regenerates into the 8th doctor.
The only Classic Doctor Who episode in which the Doctor had no companion is 'The Deadly Assassin'