It all depends how the ASIC is designed. e.g in past I used Gridseeds to mine scrypt coins but I also could use them to mine BTC (that time I considered Scrypt mining more profitable)
so the answer is YES, you can use same HW (if such ASIC is designed for)
P.S there are also specific coins called CPU COINS purposely designed to be ASIC & GPU resistant.
With CPUs - though it has turned out that most if not all of these type coins (XMR for one example) haven't been as GPU resistant as claimed.
Most "ASIC resistant" coins try to force high memory usage, but it has turned out to be entirely possible to build an ASIC that has a lot of memory available if the market is big enough.
The performance gains will tend to be a lot less though, as shown by the Baikal and other X11 ASIC, when compared to the performance gains made by Bitcoin ASIC vs GPU mining Bitcoin.