Yes it is possible to send SysEx files to your synth using an Android device, but it depends on your Android version and your device.
Most important: your device should provide proper USB-OTG support. I have experienced that not all Android devices support this. Sometimes a rooted device is required, which for me is the same as "not supported". For example, it doesn't work on my Huawei P9 lite, but it did work on my previous P8 (until I dropped it in the water. Oops.).
It's something the specs given by the manufacturer don't make clear. There are some apps in Google Play to test USB-OTG functionality.
With my Huawei P8 and my Nexus 7 I had succes, I used an app called Midi Commander. There is a "send midi file" menu option slightly hidden in the app where you can select a syx file from your device's filesystem and send it to your device. Midi Commander
Another promising App is Syx-Lib, but my phone's Android version wasn't up-to-date enough to support this app. It requires Android 6 or higher: Syx-Lib
All these apps require a good quality USB-OTG cable. These cables are cheap, but once in a while you will get bad quality cables that don't work.
Let us know if you can make one of these apps work!
I just got myself a new Android Tablet. My Nexus7 (old version) was getting slower and slower making it practically useless.
Now I have a Samsung Galaxy Tab A 10.1 (2016) with Android 7.
And hey, hurray! USB-OTG is supported, and both Midi-Commander and Syx-Lib now work perfectly.
I have stored thousands of *.syx files for my RefaceDX that are now listed in the Syx-Lib app. I can send each of these sounds to the Reface simply by clicking/tapping on them. Syx-Lib can not send a dump request message to the Reface. You can only fetch SysEx data by pushing the appropiate buttons on an attached synthesizer, but the Reface keyboards don't have such functionality (Feature requests both to Yamaha and the developer of Syx-Lib!)
Next thing I will try: run the Yamaha Soundmondo website on my tablet with the Google Chrome browser. If I can make the Web-MIDI interface work that would make me a really happy Reface-on-Android user. I will let you know.