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Of course attaching anything will increase leakage current.
The question is how much, enough to matter? Presumably
an antenna diode would be smaller or the same as a
minimum geometry FET's drain, and ungated so less leaky
than any of the transistors you use.
Diodes are meant to -prevent- antenna effect damage.
Antenna damage will cause way more leakage than the
diodes will, along with ruining reliability.