Neon rims do NOT have the same bolt pattern. The '97-'09 Neon's and SRT4's use a 5x100mm bolt pattern, which is not the same as 5x4".
5 x 4" = 5 x 101.6mm
Yes, it's enough to make a difference. If you're just looking for rollers, they'll be ok. But don't use them on the street. In most cases they will "bolt up", but they will also side load the studs when you tighten down the lugs. You may get away with that if your studs are in good condition, but you're significantly increasing the load on the studs, which increases your chances of failure. The studs (and all bolts) have a much higher tensile strength than they do shear strength.
Go to one of tbose used tire shops tbat seem to be on every corner now days. Tell them you need 4 junk tires that hold air. Thats 4 less he has to pay disposal fees on.