The bike will not start with the decompression lever pushed in....the decompression is only used to allow the engine to turn over without any compression and build up some inertia in the spinning engine parts.  Once the engine is rotating the automatic compression release turns off and allows compression....and you need to do the same thing and let go of the compression release once the engine is spinning.

About 90% of the time the bike can be started without the decompression lever....but not always.  If the engine stopped in one of the 3 strokes that do not make compression (power,exhaust,intake)....the starter motor can get some momentum built up in the crankshaft/flywheel assembly and can then power through the compression stroke.  If however - the engine is at the beginning of the compression stroke when you push the starter button....the starter is not strong enough to overcome the compression and push the piston over Top Dead Center.  (The automatic compression only works for a short period to make sure the engine has some momentum build up before the engine makes any compression).

I rode my bike for a full year without a compression release and only on occasion did I have a problem with the engine having stopped on the compression stroke.  Normally when you hit the the stop button or turn off the key you can hear the engine slowing down....and at the very end you hear the "whine" as the engine comes on the compression stroke and then spins backward.....so the engine has turned backwards away from the compression stroke.  When the engine did happen to be on the compression stroke and I hit the starter button the starter would "stall"....and I instantly let go of the starter button, put the bike in gear and rocked it forward until it was off the compression stroke.....then put it back in neutral and hit the starter button again.

Now that I do have a working manual compression lever I often only use it when the engine fails to turn over without using it.

Although you can get away without using the compression lever most of the time - you have to remember Suzuki designed this bike to be easy to operate, and start by just pushing the starter button....and it needs to do that in 100 degree weather.....or at 10 degrees below zero.  It needs to do it with a brand new battery.....and one that is nearing the end of it's useful life.  It needs to do it when you stall in heavy traffic.....the automatic compression release needs to work without you thinking about it. (A manual one requires you to do one more step while starting the bike).