The answer is YES.
Android is basically built upon Linux kernel which does utilize mulit-core.
As far as single-threaded-application is concerned, remember that a thread can not be executed in-parts on different cores simultaneously. So although your single-thread can be executed by different cores at different point in times, it can not be sub-divided and executed by different cores at the same time.
Having said that, please be aware that chipset manufacturers like Qualcomm are developing intelligent processors capable of sub-dividing your single-threaded app code (if and only if there are mutually exclusive parts) into multiple threads and have it run on different cores. Here again, the basic principle remains same – in order to utilize multi-core, the single thread was sub-divided into multiple threads.
To get the most out of your multi-core chip, you would rather create a multi-threaded app, with maximum possible asynchronous threads, so as to have optimum utilization of maximum number of cores. Hope this clears.
EDIT:
This also translates to – An app that does not make use of multiple asynchronous threads (or any other parallelism construct) will NOT use more than one core.