Can the order of filtering and downsampling be exchanged?
In Short: The order does matter.

Detailed:
Downsampling by a factor of 2 without filtering, will cause aliasing in frequencies of 500Hz and more.
Since your signal is bandlimited to 600Hz, the frequency range of 400Hz-500Hz will be corrupted.
So (theoretically) the frequency range 0Hz-400Hz will be the same with or without filtering.
If you were only interested in this range, it would have been possible to avoid the filtering.