I recognize 11 guys as being white. So, 11%.
7 white faces in 351-400 (sorry Najera, you count) -- 14%
If you stop right here, you see that of the bottom 150 NBA players, only 18 are white. 12%
13 white faces. 26%
This is the key point -- 11th men through 16th men are covered by 301-500. 15.5% of these players are white-ish.
9 white faces plus Yi Jianlian -- 18-20%
14 white faces. -- 28%
7 white faces -- 35%
5 white faces so far and they have announced up to #164 -- 5 of 17 = 29%.
Looking at spots 164-300 (137 guys), 35 of these guys are white-ish. So 25.5%.
Conclusion -- The NBA teams do not pad the end of their benches with white players to boost fan interest.
In fact, the percentage of white players from 6th man to 10th man is nearly double what you see from 10th man to 16th man. If NBA clubs wanted to bolster their benches with white guys, it would seem likely that they could find white guys at roughly the same 25% rate that you see at 164-300. You do not see that happening. If anything, you see the opposite.
The bottom of the bottom (401-500) has very few white players. The reasons for this have not been analyzed by me. It may be that marginal white players self-select out of being 11th to 16th men in the NBA in favor of some other opportunity. It may be that white players only stick with basketball over the long haul if they are very clearly pro material. Or it may be that white players who are marginal players are somehow discriminated against on the very basis that they are, well, white, and lack certain physical gifts and "upside potential" necessary to keep them around for a further look.
In any event, the myth that white guys are kept around to pad the end of NBA benches does not appear to be borne out by the ESPN 164-500 player ratings.