You may be able to get this to work provided you try not to wet the carpet too much and use a high foaming soap solution that requires a lot of rinsing, which will - yeah, wet the carpet too much and get down to the pad underneath..
I have never found a "carpet cleaning solution" such as what is sold under that name or others do much more than foam like crazy, and be really hard to rinse completely out.
You will know its not all gone if the carpeting dries "hard", and does not look right. It is still full of soapy mixture and will just attract more dirt that will not go to the bottom of the carpets and they will look dirty really faster than normal..
It will always be better to vacuum A LOT, brushing the carpeting in different directions as much as possible to get as much embedded stuff out of the bottom of the carpets.
Then, hopefully, use a low foaming really good APC, I like to just spray it on lightly, then use a good brush like the Tuff Shine white bristle tire brush, and get this into the dirty places, and then come back and steam, rinse lightly, and extract..
You can still do most of this process and get great results, but you will need to be careful, and patient with the Bissel which does not have a huge amount of water lift, and press down, and wait for it to start moving the moisture laden with whatever you moved up with the brush process out..
Good luck with this !
Dan F