Yes, i strongly believe it does. Some say it doesn't.
In theory there must be some dependancy between GPU speed and memory speed, and setting up different clock speeds should show which of both is the limiting factor.
Taking in account that it's difficult to determine how different clock settings influence game performance due to the sheer amount of cross dependencies, i simply tested different clock settings using Ati Tray Tools' internal benching facility with my Sapphire HD 3870 Dual Slot.
Common clock-settings sorted by result:
GPU/Mem (MHz) Result, Comment
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904.50/0999 = 14219,20 very high GPU, low mem
776.25/1125 = 15891,41 reference GPU, ref mem
904.50/1125 = 16063,80 very high GPU, ref mem
796.50/1152 = 16274,39 S.Toxic GPU & mem
796.50/1197 = 16773,16 typical OC GPU & mem
823.50/1197 = 16910,54 typical OC GPU & mem
850.50/1197 = 17018,82 S.Atomic GPU & mem
695.25/1341 = 17370,40 low GPU, extreme mem
850.50/1251 = 17661,97 high GPU, high mem
904.50/1251 = 17887,53 very high GPU, high mem
776.25/1341 = 18068,95 reference GPU, extreme mem
850.50/1296 = 18105,02 Atomic GPU, very high mem
904.50/1296 = 18488,85 very high GPU, very high mem
904.50/1305 = 18560,28 very high GPU + 0.0, mem + 9
904.50/1323 = 18758,06 very high GPU + 0.0, mem + 27
918.00/1323 = 18851,14 very high GPU + 13.5, mem + 27
918.00/1332 = 18921,22 very high GPU + 13.5, mem + 36
931.50/1332 = 19003,25 very high GPU + 27.0, mem + 36
945.00/1332 = 19077,39 very high GPU + 40.5, mem + 36
931.50/1341 = 19107,60 very high GPU + 27.0, mem + 45
945.00/1341 = 19188,50 very high GPU + 40.5, mem + 45
945.00/1350 = 19290.98 very high GPU + 40.5, mem + 54
958.50/1350 = unstable very high GPU + 54.0, mem + 54
Highest stable test so far:
Attachment 14433
I also tested some extreme combinations to find an optimum ratio between GPU and memory clocks which can be described as a sweet spot. It's also clear to see, where limitation steps in. Optimum ratio seems to be between 9/13 (reference clock ratio) and 2/3 on first sight, but even at 776 MHz GPU an extreme memory overclock shows how important bandwidth is for the HD 3800 Series.
Hope this tests can help to decide which overclock should work best, or wether or not a given model can be expected to be a good choice. My advice: stay away from GDDR3 or models labeled as turbo or oc, which IMHO are not as fast as you would expect.
Depending on heatsink (mine did all this tests at 45 degrees) and different voltage regulators all HD 3870 should reach nearly 900 MHz and due to the specs of GDDR4 all should reach 1250 MHz without voltmodding.
Comment if you like, or add different clocks if you wish. I will add them to this list.