It seems to be hit-or-miss with foreign recipients, although mostly "miss". I have 7 British groups with US Bronze Stars and only one has the certificate. In that case, the service recognized was from August 1943 to March 1945 and the certificate was dated 27 April 1949. I don't know if the absence of the certificates indicates that they were never sent, or if the recipients filed them away and, because of their size, they simply stayed separated from the group. Because many of the Bronze Stars originated in units that disappeared at the end of the war, many of the follow-up actions necessary to get the certificates produced simply never happened.
Of 7 Legion of Merit groups to British officers in my collection, 4 have the original certificates. Since those awards camr from the War Department or Navy Department, there is probably a greater likelihood of the certificates accompanying the medal.
OMSA 1136/DM 16