Centaurus,
The accidental bleeds off flight, or any other pressurisation panel cock-up, is one of the issues that is addressed by the new Boeing Normal Procedures. The after take-off checks now require that you specifically check the bleeds and the packs. See
http://www.b737.org.uk/nnp.htm for the full description.
AFTER TAKEOFF
Engine bleeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . On
Packs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AUTO
Landing gear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . UP and OFF
Flaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UP, no lights
BTW when I was a brand new F/O on the 737 I once ferried an aircraft to an airfield about 100 miles away. We noticed that the engines were quite slow to start and put it in the tech log at the other end. We were describing what happened to the engineer when he gave us a withering look and said “Did you fly here all the way with the bleeds off?” – the switch position confirmed that we had. The engine bleeds switches were very rarely moved and I had missed the fact that they were both off in my cockpit preparation. Since the pressurisation panel checks were read and responded to by the person who set it up (me), it was never picked up. Good job it was not a longer flight where the cabin would have had to pressurise.
Re the aircraft maintaining some pressurisation without the packs being on, I agree with BOAC that it probably depends upon the leak rate of the individual aircraft. The simulator test that you did probably assumed a leak rate of 2000fpm (-500: 2250fpm) which is the Boeing limit. On airtests I have seen leak rates vary from 1500fpm to over 4000fpm on aircraft of a similar age.
S&L