Packets are processed in sequence. So yes, you can save any number of files simultanously.
However, depending on the filesystem, doing multiple (smallish) writes might result in massive seeking between the physical write locations. With such filesystems it is faster to actually write files in sequence.
Smarter filesystems such as PFS cache the writes in a way multiple writes don't slow the overall performance.
For best overall results you should do your own caching: that is collect the smaller writes to a larger buffer, and only ACTION_WRITE the buffer when it gets full. Buffer size should probably be at least 4K, but even upto 32K or 64K can still improve performance. This is with tons of small writes and large result files.