I doubt it would do any harm to apply fake tan on a week old tatt as it should have a good scab on it now. If however it hasn't I wouldn't suggest it as it may irritate the skin and thus affect the quality of the tattoo, i.e. making the ink blotchy etc.
If you really can't resist applying the tan then maybe apply vaseline over the tattoo to create a barrier between the healing tatt and the tan :o)
Should do the trick.