Quick answer would be "probably". Since you won't be painting and entire car, you may be alright spraying each piece and letting the compressor catch up. Won't be the best situation, but you can make it work. You would be much better off with a single stage, oiled compressor that puts out 10-12 cfm @ 90 psi. That's the sweet spot for an LVLP gun. Here's a link to a Kobalt from Lowes that would fit the bill without breaking the bank.
http://www.lowes.com/ProductDisplay?...1&rel=nofollow If you can throw an extra $100, you could move up to a Ingersol Rand at Tractor Supply.
http://www.tractorsupply.com/air-com...ressor-3496111
I've sprayed with HVLP, Conventional, Compliant and LVLP guns. The HVLP and LVLP guns are slow. If you are not familiar or comfortable spraying with a particular type of gun, you won't notice. LVLP can spray as nice a finish as the other types, as long as you have a handle on it. Here's a few LVLP guns that won't break the bank.
http://www.spraygunworld.com/product...%20EVO4014.htm
http://www.amazon.com/Ampro-A6034-Pr.../dp/B0019MSJ06