Yes, they could probably even tell you who put it together, their tracking is so specific.
two more hints-
there are two dials stamped in the back of the shell. They say the month and year the shell was made. It's not exact, but if they are later than 03/06, you'll know for sure it's not March.
another is the label inside the seat area of the shell. There should be a sticker by the LATCH storage slots by the child's hip (like the seat bight). It will say whether it's a taupe or gray shell and should have a date and initials. I have a picture of one, hang on.
for instance, the shell from the Barnum Couture I have in my garage says 11/05. The date on the sticker inside says 11/14/05 and the official DOM is 11/15/05.
ETA: here are pictures (click to enlarge)-
inside the seat
back of shell (which is behind the black belt guard and can be off by a month or two)