Most (though not quite all) Android devices support operating the USB port as a USB host, either triggered by the usual OTG role pin on an adapter cable or by vendor-unique software setting. There can be various complex interactions with charging and ability to supply power to a peripheral, but for a low consumption device like a USB serial converter it will in most cases work, though obviously consuming power from the phone battery.
On the software side, Android allows Apps to interact with the USB host mode through a fairly low-level API, so in effect Apps have to bring their own user-mode USB driver implementation built with detailed understanding of how to talk to a particular peripheral. USB serial converter chips tend to be well and widely understood in the technical community, so for the major varieties you should be able to find a pre-made app or perhaps an open source codebase to leverage - but you will need one compatible with your particular converter. If you run into difficulty it may be easiest to try another - don't rule out 9-pin devices with a 9-to-25 pin adapter.
The last level would be having serial line settings and data interpretation compatible with the //e and whatever you are trying to do with it. This is where starting with an open source Android App could be beneficial as you could then customize it to best support what you are doing with the Apple.
As an alternative to USB, you could also look into using a bluetooth to serial module (on Android, classic BT would work better for this than BTLE), or perhaps making a serial-to-wifi bridge out of a small router or something like an ESP8266.