This is not quite an answer to your immediate question but thinking about this some more, I reckon that registering as unemployed might actually benefit you. Obviously, I don't know what the rules are going to be and I cannot predict what will happen when the UK effectively leaves the EU but it seems reasonable to assume that people with “permanent residence” will be in a more favorable position.
Now, to become a “permanent resident” under EU law, you must make use of your treaty rights for 5 years. And the crucial detail is that leaving the country can reset the clock but being involuntarily unemployed does not. Specifically, article 7(3) of directive 2004/38/EC reads:
- For the purposes of paragraph 1(a), a Union citizen who is no longer a worker or self-employed person shall retain the status of worker or self-employed person in the following circumstances:
(b) he/she is in duly recorded involuntary unemployment after having been employed for more than one year and has registered as a job-seeker with the relevant employment office;
(c) he/she is in duly recorded involuntary unemployment after completing a fixed-term employment contract of less than a year or after having become involuntarily unemployed during the first twelve months and has registered as a job-seeker with the relevant employment office. In this case, the status of worker shall be retained for no less than six
So unemployment is not an issue per se but, most importantly, registering with the relevant agency is a requirement to be considered a worker. During that period, you are still entitled to health insurance and fall under the rules for workers, which means that you have a right to stay irrespective of income (whereas economically inactive persons can be asked to show they have health insurance and sufficient resources to avoid any recourse to public funds).
Similarly, in a completely different context, the requirements for Niederlassungserlaubnis and citizenship for third-country (non-EU) citizens include sufficient resources at the time of the application (and not over the whole period of stay in Germany) and uninterrupted legal presence in the country. Here again, being unemployed (at least for a limited period of time) counts as legal presence and being able to document it is advantageous.
So, assuming you have worked long enough to open some rights to unemployment benefits (and ideally longer than a year), being properly registered is an easy way to document that you were still present in the country but also establish that you were still a worker under EU law, both of which might come in handy in the future.