Important to test tubes after recapping a non-working TV or radio?

[TheShanMan]

Just wondering if I run any risk of damaging components if I try firing up a radio (1946 Westinghouse) or TV (1956 Packard Bell) after recapping the chassis if the condition of the tubes is unknown? I don't have a tube tester myself although I may be able to get them tested locally. If there is little to no risk of damage then I'd like to fire them up and see what happens and only mess with testing/replacing tubes if I still have a problem.