It is only safe to put inverts in the tank when you don't use the chemicals. I just woke up to the second part of the post. Sorry about that. When you do get rid of the "undesirables" without using the chemicals, the inverts will not be affected at all and you can put them in at once. But one word of caution about adding inverts in the form of shrimp with a betta if that is what you have in mind.
As long as shrimp have their shells on they will just be harrassed by Mr/Ms. Betta as shrimp is their first food. But the time will come when they will need to shed their shell to grow a new one as the old one will get too small and the day they leave the protection of their shell chances are the betta will have a larger than normal meal. You will have nothing but a shell. Snails do not have that problem so if people want inverts with their betta I generally suggest a Mystery Snail or Apple snail, only one though as they do not bother plants and will not reproduce if there is only one in the tank where some types can reproduce prolificly even if you only have one and the tank can be overrun.
The only other snail control method that I know of is to get a group of Yo-yo loaches but then you are not able to have any type of inverts as they are all fair game and you need a fairly good sized tank for them.
Rose