No, that is not this hospidal! From 1867 to 1978, there was active hospidal (later famous IV Hospidal for Party members until they build new one next to old whitch was ready by 1978) next to Parnu street. Big hospidals at that time were next to railway and railway is just few hundred meters since XIX century from site.
We are talking three floor building whitch was build next to an old and small buliding in 1881 by L. Christophi.
Don't let this nr.12 mislead you! Today this hospidal building is still visuable and there is Magdalena Healtcentre.
Most probably in letter they are missing either "Grosse" before Peranustrasse or number was wrong or was sutch number given only to this public building.
https://firstname.lastname@example.org, ... 9wCJ_g!2e0
If you want, here is small overview in Estonian:
http://www.itk.ee/haiglast/ajalugu/magd ... la-ajalugu