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Yes they do. If you get the same signal on the same antenna (two antennae hooked up to a splitter is still one antenna), but slightly delayed, you have a problem. This is what diversity antenna systems aim to solve.

If you get the same signal on the same antenna

Thats assuming you have your antennas pointed to recieved the same signal. 802.11 protocol may not handle hearing the same signal on two antennas via a spliter, I agree.
I have seen many setups with splitters that have worked very strongly. The best setup though was not using 802.11, but Karlnet bins.

I've got a Broadcom based chipset on my Dell 1180 mini-pci card with 2 antenna connections. One says RF Main the other RF AUX. Is this the diversity type setup on this card or would I also have to diconnect one to use the other?

Not sure, what is the model of your Broadcom?

I'm not sure of the model, not clearly marked on the PCB. On the chip it reads:
bcm4301kpf
cs0235 p20
64689 s

then on the lower corner of the pcb, it has some numbers:
yr-4
94v-0

then on the silver covering on the pcb it has a Vera01.

I don't know if that would be of any help.

Looking at this PDF
http://www.broadcom.com/pbs/BCM4301.pdf

The Aux connection might be for manufacturing test only as shown on the flowchart in the pdf.

Thats my best guess.

Okay...nobody has posted why they want to split the signal to feed to antennas.

Assuming it's to get more APs, that might work, however, when it comes to actually mapping where an AP's location might be, running anything apart from an omni might throw off the actual location...not by a whole lot, but the results may not be duplicated by someone with an omni. Highway drives are probably the best example...especially if you detect APs from the HW not necessarily close to the HW.

I've found that when I have been able to see my own network via NS, the signal is far from usable to do any kind of sustained activity, and I can't do anything without a directional at those outer fringes.