I was able to find the graves of several of my family members. I did put in the names that I was looking for in English, and it found them even though there was only a Hebrew name on the stone. So, I would guess that the site does, at least,some conversion from English to Hebrew.jThat's interesting - it must be either name dependent, or cemetery dependent.
Both names I searched for yesterday were in the Kfar Saba cemetery.
I checked today :
Searched for my aunt who was buried in Haifa and has a Hebrew surname and give name with a single transliteration - and found her grave.
Searched for my Dad, buried in Jerusalem but only found his grave after I misspelled the surname: "Zlotnik" worked, "Zlotnick" (correct speling for our family) did not.
I found a Koenig, in Jerusalem (not a family member),
But did not find any Mendelowitch, (of which there more than 250 in Hebrew) not matter how I tried to spell it in Latin letters.
Conclusion: It depends on the name - and how (or if) it was transliterated