If you have buggy or misconfigured wlan router than yes. Powes saving mode support should be nowadays pretty normal thing but still some APs don't support it correctly or have it misconfigured by default. For misconfiguration look for parameters "Beacon interval" and "DTIM interval". Don't set it too high, something like 100 1 or 100 2 or 200 1 should be fine.

AFAIK devices in power saving mode wake up once per (DTIM*beacon interval) to check for new packets. On my AP I have beacon interval 100(ms) and DTIM set to 2 so the tablet periodically wake up each 200ms to get packets waiting for it in AP's buffer. So if the device is not sleeping when someone is sending packet to it, it will get the packet directly off the net and react immediately (like seen in those ping tests with power saving off or not effective). If not, access point will buffer it for the device and wake it as configured and resend all waiting packets in one go.

As for those ping tests - well this is pretty artificial test. If you really have such traffic (1 packet per second) and still require minimal latency then disable power saving or set sleep timeout interval above one second. And if traffic is continuous like this your device will not turn wi-fi chip off at all and will die in hour or so (but with low latency :-).

The worse latency seen in test proves that the tablet managed to sleep between those 1 second packets (and waked up in next beacon*DTIM period) which is a good thing for battery. This is actually a feature, not bug. It allows you listen to internet radio, browse web etc. while the wi-fi chip still manages to sleep most of the time.

If you want additional details, google for "wlan PSM" "wlan powersaving mode" or search also this forum or maemo lists for PSM timeout, or PSM interval.