And if so, why would she?
If you're not up on the Civil War [SPOILERS], you should avoid this meta.
But if you're totally fine with being spoiled, read on! So: In Peggy's S.H.I.E.L.D. file, it says that her date of birth is in 1919. BUT in the recently leaked obituary from the Civil War set, it says that she was born in 1921. Weird continuity error? Maybe...
But then again, maybe not!
While 1921 would have made Peggy 18 or 19 when the British declared War against Nazi Germany, there might have been a good reason for her to lie. In 1939, in order to serve overseas one had to be over the age of 20 (via). So, if Peggy had signed up in 1939 or 1940, she would have had to lie about her age to be able to serve on the Continent (which we saw her do in The First Avenger).