The critical point is the 'Transaction Date" ... i.e. the flight. If that triggers your promotion, you'll become Silver. When it actually shows up on your BAEC account should be irrelevant.

Happened to us a month or so ago [albeit with not quite such a tight time-line] without any problem, although it was an obvious comfort to see the process finally completed!

Qualifying flight 27 Apr
Posted on BAEC 28 Apr
TPs reset for New membership Year 29 Apr [damn, wasted 45 TPs!!]