My compressor makes the same noise when I turn it off and on though I'm not sure about startup. I have the auto climate control and its hot out right now so the AC stays on when I start up. But I'll check after work and see how it goes.
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2009 Techno Gray Metallic G6 GXP Sedan (3.6L Auto6 112K miles)
CRAB Intake Opt 3 w/FPU, Lloyds GXP floor mats, HIDs low 6000k 55w/fog 3000k 35w, LED DRLs behind lower grills, V3 Triton LED turn signal/reverse/brake, LED side markers/maps/dome/tag/trunk/high mount stop, 2 coats niteshades on tails, Tint 35% all around, Debadged (except arrows), PAC IPod and BT adapters, PowerStop D/S rotors and ceramic pads, Resonator repl w/24" cherry bomb, Racingline STB, Big 3 Upgrade, Optima Yellowtop D75/25, Blacked out arrows, chrome window trim and black dipped wheels, KYB struts and shocks, CM lowering springs, Cherry Bomb Vortex Crossflow muffler, 2.5" pipe from axle back, two 4" stainless double walled slant tips