It should be possible, I'd do it like this:
sync on
sync rate 30
hide mouse
autocam off
make matrix 1,1000,1000,5,5
make object sphere 1,100
rem This is where you set the camera output, x1,y1,x2,y2
set camera view 100,100,400,400
do
a#=wrapvalue(a#+4)
position object 1,500+(sin(a#*4)*100),(cos(a#*2)*50),500+(cos(a#*8)*25)
position camera 500+(sin(a#)*500),200,500+(cos(a#)*500)
point camera 500,0,500
sync
loop
The 300x300 box doesn't look very good, it's better using factors of the existing screen resolution, for example (640/4)x(480/4) box.