Using tails doesn't mean you wont get fingerprinted. Things such as canvas, audio hardware and harware concurrency are commonly used which don't change no matter how many oses you hop or how many vms you use.
One concept of using Tails is to not reuse the same hardware. It is portable, by design. Depending on your security priorities, this may mean use burner laptops. For the level of operation Tails offers, an old $100-$200 laptop should suffice. Some public workstations still allow you to boot off of a USB, though this may get you into trouble. Also, there are so many public and open wireless networks out there you have few excuses to reuse them.
To answer the OP's question, maybe.
Tails OS is a great starting point for a security profile. Then, if you want to use Multilogin, go for it, however, just keep in mind it will add a lot of work to remain anonymous, as Multilogin is a paid service. I would recommend finding or setting up your own proxies/vpn's rather than paying for them. Also, even using services like multilogin or tools like Tails may be enough to identify specific traffic or even a user, so do not rely on one single layer of security to keep you safe.
Also, it is absolutely necessary to keep in mind that Tails OS will do it's job, but if you reuse accounts, or writing styles, or other online habits you will out yourself, or burn your own anonymity.
I would also advise anyone serious about remaining anonymous to have multiple Tails OS intances ready to go, as part of your basic kit.