If there's a rad shop nearby , get them to resolder and test it . Most times if a side bracket has been loose , check the corner tubes for whitish marks (weep marks/calcium deposits) where they attach to the top and bottom tank . Without the support of the side bracket the expansion and contraction will loosen the corner tubes . You wouldn't want to install the rad and find out it leaks .

When I worked at the rad shop (32yrs), the procedure was a soak in the caustic tank to loosen scale , reverse flush rad & check flow , if the flow was questionable then the top tank was unsoldered from the core and the core was rodded out . After the tank , header plate was blasted and retinned , & tube tips retinned & the plate would be soldered on then the tank , connections brackets etc . Then retested by plugging the connections and hooking up 15-18 psi air supply and dunking it in a test tank of water . Sorry for being long winded , you may be lucky and the tubes won't leak but maybe expect the other scenario . George .