Entirely depends on how precise the translation is and how it is used
If it is not connected to any sort of mental link to indicate intended meaning, then it will have to rely purely on KNOWN nuances of the language, which implies that there will be a standardization of sorts. It is pretty much a normal aspect of human speech that we all develop multiple ways of speaking depending on who we are addressing. We normally refer to these as formal and informal, although they can be divided up within those categories as well.
A translator that is not tied to intended meaning will essentially establish a baseline for the formal speech. Even if it includes slang in its database, the point of slang is to convey nuance, and it is constantly changing for that reason. As slang becomes used frequently enough to be added to the official lexicon, it ceases to be slang. An example might be "good bye" which essentially started as shorthand for "God be with ye". This is a fairly consistent iteration of the phrase as the equivalent in languages like Spanish and French, "adios" and "adieu", as they both literally mean "to God" in each language.
You end up running into changes in how people speak in order to intentional create slang, or also to subvert the translators. A good example of this is the sudden rise of the term "unalive", which people use on social media to subvert filters that will suppress usage of words like "kill", "suicide", "murder", and "dead". In a similar vein, people may begin to use terminology in order to more properly convey their meaning as the recipient might receive it rather than how it is translated. This will quickly change languages in the sense that they will start to use terminology and phrasing and speech patterns that may have been odd before, but will function better for the translator.
The greater concern might be about which point the translator comes into use in peoples lives. A big part of speech development is exposure. People pick up their families accent because that is their primary exposure, but their accent may shift if they are exposed to others. Therefore, if they are never exposed to any other accent, and/or they are heavily exposed to translated speech, they are likely to develop a monotone speech pattern or possibly a stagnation of dialect development.
Conversely, lack of exposure beyond close relations may cause a further splintering of dialects as it may quickly separate within the family as every family develops there own slight differences, usually with small children. This is probably most obvious in the thousands upon thousands of iterations of grandparent nicknames, or different terms for pacifier. Imagine if every generation used only nicknames for a whole generation and without any outside exposure, the proper terms would quickly become practically a foreign language.
Realistically speaking, it will probably be a massive conglomeration of each possibility as the translation will affect different people in different ways.
How would the translator know the nuance of Japanese honorifics as they need pre-existing knowledge of the relationship between the speakers? How would it understand when an expletive is being used positively or negatively if both sentences make sense? How will it convey tone of voice or the nuance of speech patterns that are normally recorded in punctuation? Some individuals may not be exposed to universal translators until adulthood, while others will have them their entire lives. Imagine if two parents never learned each others languages and only communicate via translator, but their child develops a sort of pigeon or creole that neither parent understands independently as the translator always offsets the differences.
It's also entirely possible for people to learn to read and write in one language while speaking something completely different and being completely unaware of the differences as there are numerous languages that are non-phonetic. You could standardize a single written language for the whole of the galaxy, but then two individuals could pronounce it in totally different ways that are completely unintelligible to the other. At the end of the day, universal translators would simply be another factor in language drift, but not necessarily make it anymore or less complex.