Consensus
So no rule comes out and says this, to my knowledge, but the universal consensus, in my experience, is No.
We see this reflected in monster stat blocks: you won’t find one where the same limb is shown attacking multiple times in a Full-Attack entry. Rather, the statblock will list several independent options, where the monster uses its weapons in one and doesn’t in another. The marilith is a typical, albeit extreme, example:
Full Attack: Primary longsword […] and 5 longswords […] and tail slap […]; or 6 slams […] and tail slap […]
(Monster Manual pg. 44)
The 6 slams replace the primary longsword and 5 secondary longswords here. We see the tail slap listed in both versions, since the tail isn’t wielding a weapon. But the marilith doesn’t slam with the arm that swung a longsword.
Other monsters are similar. So while this rule isn’t actually found in the text, we see how Wizards of the Coast themselves abided by it.
General Rules
But for the actual rules, all we get is this one paragraph (found in the Monster Manual as well as Rules Compendium):
Some creatures combine attacks with natural and manufactured weapons when they make a full attack. When they do so, the manufactured weapon attack is considered the primary attack unless the creature’s description indicates otherwise and any natural weapons the creature also uses are considered secondary natural attacks. These secondary attacks do not interfere with the primary attack as attacking with an off-hand weapon does, but they take the usual -5 penalty (or -2 with the Multiattack feat) for such attacks, even if the natural weapon used is normally the creature’s primary natural weapon.
(Monster Manual pg. 311; Rules Compendium pg. 100)
It clearly describes mixing manufactured and natural weapons, and the manufactured weapon counting as the “primary” and all others getting relegated to secondary status. But it doesn’t describe the limitations on one’s limbs.
I think this may have been addressed directly in a Rules of the Game article on Wizards’ website, but those are difficult to search now that you have to go through the Wayback Machine. I’ll keep looking for it, but ultimately it only matters so much: the Rules of the Game articles aren’t rules sources, they’re (supposed to be) explanations of the rules. Anything said in there that isn’t said in the actual rules is suspect (and at least a few things are wrong, or at least bad ideas).
Thri-Kreen in particular
It may be relevant to you to point out that the thri-kreen is another typical monster that avoids repeating limbs in its full attack entry:
Full Attack: 4 claws […] and bite […]; or longspear […] and 2 claws […] and bite […]; or javelin […]
(Expanded Psionics Handbook pg. 213)
We see here that when the thri-kreen uses its two-handed longspear, it loses two of its four claw attacks to do it.
Thus, even if one were to try to quibble about primary sources and so on in the general case, for thri-kreen in particular I think it’s a lot harder to argue that you could use claws that have already attacked with a weapon.