Conor;
Hi! Wirbelwinds (Flakpanzer IV Wirbelwind; 2cm flakvierling 38 auf fahrgestel Pz.Kpfw. IV) and zimmerit...
As I think has been noted above posts, the wirbelwind was a conversion of an older Panzer IV to a flakpanzer, created by swapping a large open-top flak-turret and gun assembly in for the normal long-gun "MBT" turret. These fabrications were built by OstBau Werke - Sagan starting in mid - later May 1944, with somewheres around 85 - 100 or so being completed by NOV 1944, when this production ceased. OstBau used available running hulls obtained from units turning in badly-damaged Pz IV for refurbishment. Different sources variably indicate that these tanks included Pz.IV Ausf. F, G and H, and some early J hulls.
So, did wirbelwinds get or have zimmerit? YES - many did, as seen in various period pics. It seems likely that zimm'd wirbels had zimm because they were built on tanks which already had zimm - as there is no clear record that OstBau did any zimm application during their rebuild process. From this, knowing whether the original base hull was an F, G, H or J matters.
As a matter of record, no F or G received factory zimmerit, as these were all built prior to SEP 1943, when factory zimm application started. The first 1000 or so H also "escaped" factory zimm, for the same reason. Later H and all J hulls used for wirbels would have been factory zimm'd. As to whether ANY Pz IV was actually "field-zimm'd"... any such job would likely have really been a repair shop event and not some crew effort conducted between shell-bursts. There probably were a few, but this may not matter for this!
IF the question is about Wirbelwinds at Normandy (ca June 06 - 20, 1944?) and whether any would have had zimm... there simply cannot have been many wirbelwinds there by 06 June 1944 if they only started production in mid-May over in Silesia (Sagan). Of whichever few there could have been, probably some were zimm'd, based on the guess that it was "first in - first used" for the hulls sent to Sagan.
So... IF you decide to build a G wirbel, then it most likely had no (factory) zimm (and there is a recent Dragon Wirbel G kit exactly for this!). And then there are available both wirbel H w/ and w/o zimm kits... and you (like I w/ my ancient Tamiya rendition of this thing) always have the option of adding your own!
Seems like you have some choices - albeit not much record for wirbels in Normandy in early June, 1944!
Bob