Well not exactly, but according to the American Heritage Dictionary of the English Language, impregnable means:
1. Impossible to capture or enter by force: an impregnable fortress.
2. Difficult or impossible to attack, challenge, or refute with success: an impregnable argument.
Or, according to Wiktionary's short definition:
(Of a fortress, wall, etc.) Too strong to be penetrated.
On the other hand, the meanings of impregnate, in addition to "make pregnant", include
3. To fill throughout; saturate: a cotton wad that was impregnated with ether.
4. To permeate or imbue: impregnate a speech with optimism. See Synonyms at charge.
2. to make a substance such as a liquid spread all the way through something: a pad impregnated with natural oils
1. a : to cause to be filled, imbued, permeated, or saturated
b : to permeate thoroughly
which, at a stretch, are closer to the "penetrate" meaning. Hence the question in the title.
Why is this? I guess it's because, as with inflammable and flammable, the two words come from different meanings of the in- prefix; impregnable from a "negation" meaning and impregnate from an "into" meaning. (And indeed, the AHD gives etymology with in-1 for impregnable, and in-2 for impregnate.) Is this right?
Some dictionaries also list a meaning for impregnable that come from impregnate and seem the opposite (in a loose sense) of the meaning above: the same AHD gives, as its second definition for impregnable,
ADJECTIVE: Capable of being impregnated.
and some Hutchinson's Dictionary of Difficult Words gives:
a. able to withstand attack; capable of being fertilized; able to become or be made pregnant.
Are these "capable of being impregnated" meanings for impregnable common?
[Finally, if one does want to express the 'easily penetrable' meaning, as in "This badly designed bulletproof jacket is easily penetrable", can one use "pregnable"? "non-impregnable"? Is there risk of confusion that "pregnable" may mean "can be made pregnant"?]