There are many companies who have built a multi-tenant solution like the one you describe using Mendix. If you look in the app store, you will see a number of these. You will have architecture decisions to make, primarily around security, to enable such a model. But this is definitely something that can be built using Mendix.
Answer longer than comment allows:
If you want to charge them that way you could. However, you would need to create a separate App (model) for each customer as you cannot deploy more than one app to the Sandbox from a single Mendix business model. Also, the sandbox goes to sleep after 2 hours of non use, will wake up when someone logs in. Sandbox also doesn't give you the kind of backup and restore capabilities I think you would want if you are offering a paid service to customers.
Finally, I am not sure that this kind of usage complies with the Mendix license agreement you consented to when you created a Mendix account. However, I am not a Mendix employee, so can't confirm that.
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