The Amateur Draft is in the middle of the season like RL.
You will have to allocate enough money in your budget to cover the contracts to which you've committed. I don't think you'll be able to acquire a player if his season 2 contract puts you over your season 2 limit, so your scenario can't occur - I believe you can only spend up to 80% of your budgeted Player Payroll on season 2 salaries, regardless of the amount you acquire through trades.