Plex is a server, same as Serviio. There would be no benefit to feed one server from another. Plex also has DLNA functionality, so you'd only be duplicating the processing necessary to stream the media. So no, you can't use Plex to feed media to Serviio.
However, there's no reason you can't configure the same media locations to both servers, and run them both. Even on the same computer. I do this for one primary purpose. When I travel, I can use the Plex channel on my Roku I take with me and watch my own media in my hotel room. I can do this with Serviio, but it requires connecting my laptop to the hotel TV via HDMI, and there's no way to control it while reclining on the bed. With my Roku and Plex, I use the remote the same I would on any home TV.
Why don't I just use Plex for my home use as well? Because I prefer the functionality of Serviio, the ability to easily customize the profiles if needed, and I just plain like it.
EDIT:
I just read your message again after I posted, and I now see you were referring to using the Plex app to view media from Serviio. Unfortunately, no there's no way to do that. Their player app is specific to Plex. However, what Serviio looks like on your player is up to the player, not Serviio. For example, my Samsung TVs have a terrible DLNA player interface. There's nothing but the movie name and the cover image. On my Roku, the same media has the name, year released, run time, rating (G, PG, PG-13, R), and the video format and resolution. Along with a much larger and higher quality cover image. So you might consider a different player.
Dan
LG NANO85 4K TV, Samsung JU7100 4K TV, Sony BDP-S3500, Sharp 4K Roku TV, Insignia Roku TV, Roku Ultra, Premiere and Stick, Nvidia Shield, Yamaha RX-V583 AVR.
Primary server: Intel i5-6400, 16 gig ram, Windows 10 Pro, 22 TB hard drive space | Test server Windows 10 Pro, AMD Phenom II X4 965, 8 gig ram
HOWTO: Enable debug logging HOWTO: Identify media file contents