A custom ROM on Android is usually a modification of the factory edition, a port from a different phone running the same kernel and Android version, or a cross-port to upgrade the version by merging needed firmware files with the new release. Sometimes if the custom ROM builder is intelligent enough, they'll build a complete ROM from the AOSP (Android Open Source Project). However, that usually requires access to kernel source and most manufacturers don't release this unless required by law.
To define a custom rom as a modified stock system with proprietary software removed for copyright compliant releases, then iPhone also has custom ROM's (firmware) because you can jailbreak an iPhone and modify the system to "customize it".
So, you can build your own custom ROM that is specifically designed to remove any Google data collecting software on Android, as Android is an open-sourced project, you can modify it to build your own OS if needed (one with removed Google data collecting software).
However, I assume from your question that "you don't want to be tracked in any manner".
Google has several methods of data collection, for example if you prefer to use Chrome then data analytic software will collect a lot of information about your browsing habits (for improvements to the software) and to be sold to third-party data-miners.
Even if you don't use Chrome and avoid using google.com and any related websites/companies or softwares, you'd still potentially have data collected by other applications and websites that'll sell this information to a global analytics company (usually AXIOM). The company releases information back to Google and Google can still "track" you regardless of your product choice.
For example, Facebook is also a company that provides personally identifiable analytics to AXIOM, that can and most probably are purchased by Google and nearly any other company working on artificial intelligence since it needs data to learn.
Anyway, you can remove a lot of data collecting software, but it's only going to either increase someone's interest in your device usage (Google) or end up causing data to be collected more often.
For example, if you used purchased software, it'll be constantly logging to Google that you haven't purchased it, this is because it's constantly connecting to Google's servers to check for purchases by your account, and reporting that it can't verify the purchase because it's missing the Google Play Services application. In time, this should increase someone's interest (Application Developers - Google - Others).
The question is, why? If you need to stop it from collecting your habits, try using alternative methods, like using DuckDuckGo.com (a search engine that doesn't track you).
Turn off unnecessary data collection in every application that you can
(sometimes the switch to turn off analytics is hidden in weird pages like help and info, etc.)
So to answer your question in one line: No, Google has other means of personalized analytics.