If they came back to with a search warrant looking for gear and didn't find anything, no, you couldn't sue them. If a judge issues a search warrant he will only do so if there is reasonable cause. If there is reasonable cause for the search, even if they don't find anything, you do not have a recourse of action unless you can prove without doubt that there was no reason for probable cause...that is very hard to do.
If they had come to your house searching for the girl the other night and your gear had been in plane sight, they could arrest you even though they were not there looking for it. For example, if a cop pulls you over for running a stop sign, if that's the only reason he pulled you over but in doing so finds you to be under the influence, even though he only pulled you over for running a stop sign, he can now arrest you for driving while intoxicated.
Now, if when they came last night to search for the girl if they had opened your box and found the gear, any lawyer worth his salt would be able to get this thrown out, this would be an easy case of an unreasonable search. If an unreasonable search can be proven, it is protected by the U.S. Supreme court. This came about from a case in the 1961 Mapp vs Ohio where unreasonable searches were deemed a violation of the 4th amendment. In this case they were looking for a suspected bomb fugitive but while searching they came across a chest of illegal pornography. they arrested her on that charge but it would not stick once it reached the U.S. Supreme course since the material found was done so in an unreasonable way and because it was not the reason they went to her house in the first place.