Sympathetic stimulation will initially increase the cardiac output by increased contractile force.
The decreased filling does not become evident until a much higher, unsustainable heart rate (or a sustained tachycardia for an extended period).
This is why dysrythmias such as SVT are dangerous, there is not enough filling time and the overall CO decreases to a subphysiological value.
So you are right, but the ionotropic effects are much more appreciable than the chronotropic effects - unless it goes on for too long, or the rate gets too high.