Yah more or less. Give any political set up enough time and the ideology that set it up (if any) generally diminishes (for a whole host of reasons like population flux as you mention)...but there will be remnants.
Not too far from here is a collection of forts and canals lining the st lawrence and its connection to the Great Lakes....the British invested heavily in them, especially after the war of 1812 which showed how vulnerable the logistics network was to American intrusion. They even moved the capital more inland (and constructed a separate canal system to it) so it would buy enough time to put up a defense after Fort York + settlement (now Toronto) was easily assaulted (across lake ontario) and burned (legislature building and all) by the US forces. It is really an era much forgotten (esp after the US had its own civil war a half a century later)....and with it the core ideology is tempered with time.
Politically probably the most significant remnant of the difference in these ideologies (past the different setups, one parliamentary the other presidential) is the concept of inherent inalienable rights found in the US declaration of independence and highly influential in their constitution (esp the 1st and 2nd amendments)...and one of long storied and rich debate in their supreme court.
These were made largely specifically to contrast with the Crown system which of course vested powers over time away from an earthly monarch (Magna Carta and onwards)....but never recognised inherent (pre-existing) rights.
Very few people actually grasp the significance of this difference today....civics is no longer really taught in either country....and thus the action of entropy/time from the founding ideologies lurches on and on....it seems quite inevitable (its not all necessarily bad, but it is quite noticeable to those that have strong interests in history, politics and economics like myself).
Right now I am doing a significant study into Rome in my spare time, and there are many parallels both with its rise and fall....as time acted upon the edifices of its original core ideologies.
@Joe Shearer @Jungibaaz