Is it bad for the computer to configure not to download JDKs and Maven Libraries(in the shared indexes settings) and use local indexes in IntelliJ IDEA?

Your project will continue to work fine, but the indexing time may increase.

Shared indexes were designed to reduce the indexing time. Unlike the regular indexes that are built locally, shared indexes are generated once and are later reused on another computer whenever they are needed. Please see https://www.jetbrains.com/help/idea/2021.1/shared-indexes.html, and https://blog.jetbrains.com/idea/2020/07/shared-indexes-plugin-unveiled to learn more about this feature.