Sure. I'm not fluent in 日本語, but I know a little and I learned the meaning of plenty of kanji before I knew the reading, and for many kanji, there can be multiple readings, as well. (onyomi and kunyomi)
In fact, a fairly popular way to self-teach Japanese involves utilizing a book series called "Remembering the Kanji", which teaches the meanings of kanji without any readings at all in the first volume. People are able to comprehend quite a bit on a basic level after volume 1 - no grammar and no way to speak or understand spoken word, but generally enough to get a rough idea of texts published at a fairly basic level.
However, I imagine most people at this point, for most words, are probably subvocalizing the english word or meaning in their heads. It's pretty common, even for people that know the proper pronunciation, to still keep translating in their mind vs. just using the word in the foreign language. Personally, I really only subvocalize the Japanese pronunciation for words where they aren't really directly translatable. Kawaii is a good example - it's easy to just translate as 'cute' and it's a word a lot of non-Japanese speakers know, but it doesn't really convey the full meaning of the term and all of the cultural aspects of it. Shikataganai/shogunai are another common example. Phrases and words that don't have accurate direct translations are generally the first people learn to think of totally in their secondary languages, and a lot of people never progress beyond that.
Which is a long way of saying it's hard to tell on this because someone who knows another language could be subvocalizing in their primary language, and someone who only knows the non-alphabetic language but can't pronounce it is pretty unlikely to exist, since most kids learn to speak and hear before they learn to write and read.
The exception would be people that are born totally deaf - and then you don't need to use a non-alphabetic language. They wouldn't know the sounds to be able to subvocalize them even in an alphabetic language.
Doing some quick googling, it looks like even some people that are born deaf develop a subvocalization alternative, with pictures, sign language, etc., though some do not develop the habit at all: https://books.google.com/books?id=8PhwXf9uj1IC&pg=PA114&lpg=...