I agree that they have a "smallish" fanbase considering that they are an established mid-to-low end epl club. But, its still not abnormally low given their status relative to other clubs with a similar status.
I believe with investment in their playing staff, the size of the fan base will grow. People are attracted to glamour and success, and if Khan can bring this to Craven Cottage, i beleive new fans will come.
I think this because i don't agree with the statement: "fans are the only ones who show any loyalty in football". Although it is a bit of a generalisation. I think "no one has any loyalty in football" is a far more accurate representation of reality. This is because, we see clubs like Leeds and Portsmouth drop down the leagues, and guess what? their attendance figures dropped too. Conversely, when you see newly promoted teams their fan numbers increase. Ie. look at Fulham and Wigan. Compare the attendance figures of these clubs when they were in the 3rd/4th tier, with their epl attendances.
Hence, i strongly believe, as long as Khan brings success to Fulham, in the long-term their attendances will reflect the extent of their success.