This is the exact translation in Serbian too. (eng. she drinks milk - srb. ona pije mleko)
Does Polish have the same palatisation as in Russish? So, is "mleko" to be pronounced like "mljeko" or is it elsewhere always marked in the orthography?
No, L (unless before i) is not a palatal sound. In context of English, it's called light L.
Pronouncing L as a palatal sound may be interpreted as having come from the East.
Russian "moloko" doesn't palatalize the L. The word for lion, лев, "liew," in Russian, (spelled in Polish) does palatalize the L.
However, having said that, the Polish "L" does have a retroflex pronunciation to it, compared to an English "L" or a Russian unpalatalized Л, meaning that the tip of the tongue curls backward, touching the alveolar bone behind the teeth. In an English "L" and Russian unpalatalized Л, the tongue touches the teeth. In a palatalized Russian Л (ль, ля, ле, ли, лё, лю), the tongue curls backward even further than the Polish "L," so the pronunciation of the Polish "L" falls somewhere between an English "L" and a Russian palatalized Л
Polish uses "i" to make those lighter sounds. There is no "i" in "mleko," so it's pronounced without palatisation :).