Sure, it�s fine to use the proper amount of flux and no solder when reworking BGA.
Recognize that these new solder connections have less metal and a lower standoff than similar BGA solder connections that have not been reworked. This undoubtedly will reduce the reliability of your product, somewhat.
The issue of "the proper amount of flux" is critical. We, on SMTnet, have discussed controlling the application of paste flux when replacing BGA in previous threads. Using liquid flux is even more difficult to control than paste flux. Either way, if you put-down and leave excessive NC flux on your board, it is as risky as leaving water soluable flux on the board.
One final note: Some companies, including Motorola, do not reball and reuse BGA in shippable products. One line of thought on this is that reworked BGA see too many thermal cycles to be reliable.
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