Kerbal Space Program intuition tells me that the worst case is that you produce a high velocity piece of debris aligned perpendicular to radial vector, e.g. aligned with the existing orbit. I think this is a fairly unlikely direction to transfer energy in a head-on collision (by conservation of momentum arguments). That debris would then traverse a fairly elliptical orbit with frequent passes at the same altitude, likely resulting in relatively rapid de-orbit. The main risk would be inducing chain reaction at higher altitudes during those few passes, which seems unlikely.
Any other debris trajectory induced by collision would hit lower altitudes in less than one orbit time (either going outwards and thus on a much more eccentric orbit, resulting in lower altitude pass in less than one orbit time, or going inwards and immediately passing at lower altitudes). So that debris seems likely to deorbit even more quickly, indicating your intuition is correct.
This all makes sense once you grok why craft need two separate boosts to transfer to a higher geocentric orbit.
Of course there's a transition point where satellites are so dense that even these short-lived trajectories are sufficient to induce a self-maintaining chain reaction of debris. I suspect that's unlikely - the probability of a collision occurring in one or two orbital periods seems negligible.