Only if you buy from a dealer. Leaves a big loophole.
How do you suppose a requirement to conduct a background check in private transactions can be enforced?
Presently, there are more than 300,000,000 firearms in private hands in the USA, most of them unregistered so the government has no idea who owns any specific firearms. As such, the governement has no way of knowing whether a specific firearm has been transfered illegaly and without a background check.
Thus, a law which requires universal background checks will be one of two types:
1.) One which depends upon the voluntary compliance of honest sellers who are unwilling to sell their firearm to persons unknown to them and in violation of law; or,
2.) One which is coupled with universal firearms registration or record keeping requirements so as to provide a means to to effectively enforce the requirement of background checks.
Laws along the lines of the first type will easily pass in Congress and if they are relatively easy to comply with and are cheap, will have a ~30% compliance ratio... meaning that 30% of the private transactions which should have a background check will have a background check.
Laws along the lines of the 2nd type will not pass Congress for the foreseeable future. You want something done, then advocate passage of the 1st type of law.