Definitely possible. In the recent versions of ffmpeg they have added a -stream_loop flag that allows you to loop the input as many times as required.
The gotcha is that if you don't regenerate the pts from the source, ffmpeg will drop frames after the first loop (as the timestamp will suddenly go back in time). To avoid this, you need to tell ffmpeg to generate the pts so you get an increasing timestamp between loops. This is done with the +genpts call (it has to be before the -i arg).
Here's an example ffmpeg call (replace $F with your input file). This example generates two output streams and the -stream_loop -1 argument tells ffmpeg to continuously loop the input. The output in this case is for a similar stream broadcast ingest (MetaCDN), adjust accordingly to your requirements.
ffmpeg -threads 2 -re -fflags +genpts -stream_loop -1 -i $F \
-s 640x360 -ac 2 -f flv -vcodec libx264 -profile:v baseline -b:v 600k -maxrate 600k -bufsize 600k -r 24 -ar 44100 -g 48 -c:a libfdk_aac -b:a 64k "rtmp://publish.live.metacdn.com/2050C7/dfsdfsd/lowquality_664?hello&adbe-live-event=lowquality_" \
-s 1920x1080 -ac 2 -f flv -vcodec libx264 -profile:v baseline -b:v 2000k -maxrate 2000k -bufsize 2000k -r 24 -ar 44100 -g 48 -c:a libfdk_aac -b:a 64k "rtmp://publish.live.metacdn.com/2050C7/dfsdfsd/highquality_2064?mate&adbe-live-event=highquality_"