Yes, it is possible to use an alternative app store without root. That statement includes TutuApp, but also other similar platforms, such as Aptoide or MoboPlay App Store. The installation of an additional store, as a rule, does not differ from the installation of other applications. The first thing you need to do is download its installation file in APK format and then run it. Once finished, the new store will be available on your device.
Focusing on the case of TutuApp, we must warn you that, although it does not require superuser permissions, it does request access to some sensitive sections of your device. Beyond the permission to read and write in the storage, TutuApp will ask you to allow it to manage calls, access your location or read the usage data of your terminal. All these permissions are mandatory and, if you do not grant them, your application stops working. Likewise, although it does not do so when it starts for the first time, it may also ask for access to the camera and your contacts.
Of course, the fact that TutuApp does not require root permissions, in a way, protects the integrity of your terminal, along with that of the operating system. But the additional permissions it demands are excessive and generate a sense of insecurity. After all, the main purpose of TutuApp is to facilitate the download of applications and to fulfill it should not be necessary to read Android usage data or manage calls.
Therefore, before using TutuApp, or any similar platform, evaluate to what extent it is necessary for you and whether it is really worth providing so much personal data to download an application.