its not 100% clear-cut but the fact that there are separate sections for the regular season and the playoffs would suggest that nothing carries over (fouls or suspensions accrued from the regular season)
http://www.nba.com/media/rule_book_2007-08.pdf
Page 43:
a. The following progressive technical foul and ejection schedules will apply.
(1) REGULAR SEASON
Technical Fouls 1-5: $1,000 fine each
Technical Fouls 6-10: $1,500 fine each
Technical Fouls 11-15: $2,000 fine each (with a warning letter
sent when the violator reaches his 12th
technical foul)
Technical Foul 16: $2,500 fine plus one-game suspension
Each Additional Technical Foul: $2,500 fine
Each Two Additional Technical Fouls
(18, 20, 22, etc.): $2,500 fine plus one-game suspension
(2) PLAYOFFS
Technical Fouls 1-2: $1,000 fine each
Technical Fouls 3-4: $1,500 fine each
Technical Fouls 5-6: $2,000 fine each (with a warning letter
sent when the violator reaches his 5th
technical foul)
Technical Foul 7: $2,500 fine plus one-game suspension
Each Additional Technical Foul: $2,500 fine
Each Two Additional Technical Fouls
(9, 11, 13, etc.): $2,500 fine plus one-game suspension