Why does AC unit need condensation drain trap?
The trap in the condensate drain, prevents the unit from sucking air from; or blowing air into, the drain line. Without the trap, the condensate may not drain until the blower turns off. This could lead to the pan overflowing. So you can't remove that.

The secondary drain is typically for situations when the main drain is blocked, or otherwise insufficient.  In some units, condensate only reaches the secondary drain when the pan overflows. If this is the case, using the secondary drain as a main, would allow water to sit stagnant in the pan. So you probably won't be able to use it as the main drain, but it may vary depending on the unit.