You didn't include a clue as to the model or vintage of your 11" but according to Logan catalogs from the 1950's and 1960's, the answer is no. The taper attachment for the 11" is listed as AC-295. For the 10", AC-255 or AC-298.
I just uploaded into Downloads the 1956 Logan catalog. See whether or not your 11" is included. If it is, then what I just wrote applies. The catalog of course gives no details of what's different. The only difference mentioned is that the one for the 11" weighs 2 pounds more than the one for the 10".
Having a Logan 10 with a taper attachment my thoughts are that it would work if you make a block to raise the attachment point 1/2" higher. The carriage on an 11" is 1/2" thicker than a 10. My 10" had an 11" carriage when I got it and it placed the tool too high to get good adjustment, so I replaced it with a carriage from a 10". The taper attachment didn't fit(needed a block) with the 11" carriage, but fits now with the 10. The topslide is the same and will interchange. I have a logan/wards that was highly modified when I got it so I can't guarantee you that all taper attachments fit all lathes. My thoughts are if you are getting the 11" taper attachment at a fair price then some work to make it fit wouldn't be bad. If you are paying top dollar then maybe keep looking for a ten.
My 10 inch lathe came with the 11" taper attachment, and it operates as if it was made to fit. Mine also has the standard cross slide but a steel plate that bolts to it, so it may be that there are different "kits" that were sold for this.