That should have no effect on the fuel line
The vent to the can allows vapors from the tank to collect in the can after shutdown( keeps the garage from smelling like fuel or escaping to the atmosphere hense the first emissions).
When starting the vehicle these vapors are drawn into the carb and burned in the engine assuming it's all hooked up correctly.
The gas cap vent which allows air to be drawn into the tank if it was to become clogged the vent line to the evap can would serve the same purpose to prevent a negative pressure in the tank which can cause fuel delivery issues.
Even tho your fuel line is draining which your fuel pump should prevent to a certain amount because it is self regulated to whatever psi it delivers your carb should still hold fuel in the bowl for restart from 10 minutes to several days depending on evaporation rate.
I run a edelbrock street pump that (6psi) allows drain back after a short time with no starting problems other than after sitting a few days and the fuel in the carb evaporates, and even then doesn't take much.
The only time I had starting problems like your having is when my old stock design fuel pump was putting out to much psi and held pressure after shut down and caused fuel press to rise from heat expansion up to around 10 psi on my online gauge causing flooding by overcoming the needle/seat in the carb and hard starting warm.
Replace all your exposed rubber fuel lines from the tank to the carb and can with a quality fuel line for ethanol fuels first like bent72 has encountered cracked hose.
I use fuel injection hose.
Hopefully that will cure the problem, but if not you have other options.
Also today's crappy aftermarket fuel pumps sometimes put out to much pressure for carbs causing troubles only exasperated by ethanol fuels.