Other than the extra length of pipe between the tee and the cap, the configuration of the vent in your design is really no different than that of a typical siphon system, so I don't see why your system would need a check valve. If the air trapped in the extra length of pipe between the tee and the cap on your system's vent were to cause an issue (and I don't think it would) you could simply install an automatic air bleeder/vent on the top end of the vent pipe, in place of the cap
You've probably seen this drawing, but here it is just in case you haven't:
The drawing of typical siphon system in this link doesn't have a check valve, or air bleeder Here's some examples of automatic air bleeds:
air bleed Automatic air bleed Auto matic air bleed 2 
