No you would get your players and be placed in a mini-league with other teams that signed up about the same time. You would all be 0-0.
Instead of playing 5 league games and then spending 2 weeks playing scrimmages, you would get 10 league games. If there were 5 league games remaining, there would be 12 game dates (Tu, Th, Sa), so the mini-league might play 3 games, 3 games, 2 games, 2 games, with scrimmage dates the last two weeks. Or if it was simpler to program using the regular schedule, you would simply play the last 8 games of the schedule.
At the end of the season, everyone would be "promoted" into a regular league, with placement based on your actual performance.