In technical terms, what would happen if someone with a bunch of ASIC miners pushed their machines onto a Scrypt chain?
Obviously, an ASIC for SHA256 mining cannot do Scrypt mining.
So you are asking what would happen if an ASIC that does Scrypt were invented?
It probably depends on how the ASICs are put into play. If they are intended to be units for sale to the public, then it might be something that would benefit the leading Scrypt-based alt. If the units are intended to be used in a 51% attack, then it is lights out for whatever Scyrpt-based alt(S) they target.
I am actively looking into this. The problem is that ASIC's are not economically worthwhile for LTC yet. Although we technically have a high valuation, the markets are shallow- way too much slippage on the exchanges at the moment. If you guess that on the lower bound an ASIC might cost 100K usd to build (That's really low end too, one quote I have just for preliminary design is around 40K USD, just to design, and that's no guarantee of how well it hashes) and you mine 1 million coins super fast, you still have to sit around and hope LTC takes off to recoup your investment. If you sell those 1 millions coins, you would destroy the LTC market.
Chicken and egg really. But people are looking into it. A more reasonable start would be an FPGA but so far the results are not very encouraging.