Yes, but note that this is strategy that can easily backfire.
Your medical information is among the most high-value stuff - the data gold - that is out there (next to your financials). The companies that collect it are deeply hooked into the ‘datasphere’, and it would be easy for them to know who you are, regardless of the information you fill in (e.g. by your IP, unique ID’s and browser fingerprint).
Providing false information could then lead to you being automatically (by algorithms, no humans involved) marked as untrustworthy, ‘prone to lying’ in your ‘psycho’ profile. The automatic nature of this is most dangerous, because whereas a human might conclude you provided the false information to protect your privacy, an algorithm might not come to that conclusion and place you on some black list. Once there - without you even knowing it - it is near impossible to remove yourself from it.
And it will have consequences in all kinds of places. E.g. only yesterday there was a Hacker News discussion on how your profile data determines how long you have to wait on the phone for Customer Service (see here). This is just one example, but you could imagine how the derived/aggregated ‘Reliability rating’ could play a factor in the amount of service you receive (these support people won’t have knowledge of how that rating was produced).
So be careful with that strategy, I’d say