At least one of them, if you consider older edition info
This is partially drawn from some older information, but here you go...
As you stated, the Monster Manual says that Kuo-Toa 'create' gods by believing in them so hard that they manifest. It continues to say this...
One of the most revered gods of the kuo-toa is Blibdoolpoolp the Sea Mother, who takes the form of a female human with a crayfish head, a crayfish’s claws, and an articulated shell covering her shoulders. Blibdoolpoolp was likely invented by a kuo-toa that improved on a broken human statue by adding the limbs and head of a crustacean. In sudden awe of its handiwork, it then named the resulting form a god.
While no 5E information exists expanding on this, there is some 3E material that covers this particular goddess.
From the 3rd Edition book Faiths and Pantheons, we have a table on page 221 (list of non-human deities) that has record of Blibdoolpoolp. She is listed as an Intermediate Deity, thus being on the same power level as gods such as Kelemvor, Tymora, Lloth (Lolth), and Helm. She has the Domains of Destruction, Evil, and Water (Pared back to just 'Death' in 5E, see Appendix B of the DMG.)
The 3rd Edition book Player's Guide to Faerun gives us a little more details. On page 53, it introduces her Home Plane: The Fated Depths, which she shared with Sekolah, the god of the Sahuagin.
The Drowning Goddess, on the other hand, does have a realm—a spherical temple that resembles a small moon drifting through the unholy waters of the plane.
So, as we can see from here...Blibdoolpoolp is spoken of in the same breath and in the same manner as all other gods. Apart from the fact that she was created by her worshipers believing in her hard enough, she appears to be a fully functional deity.
Now, as for any other gods they may invent...the books are less clear. The phrasing makes it clear that a newly invented god has to reach a critical mass of worshipers before it would be possible for them to actually exist, but specific details are never provided.
Of note, The Fated Depths apparently ceased to exist during the Spellplague. We have no updated information from 4E or 5E on where Blibdoolpoolp presently resides.
