Not always, obviously, because "dick" and "dig" are different words and are distinguishable only by the final consonant. That's precisely the point. Which pairs of words in Russian are distinguishable only by the softness of a consonant?
There are plenty of words and word forms like that. стал - сталь, был - быль, лёд - лот. лыко - лика, стол -столь. школы - школе, лак -ляг, говорит -говорить, мат - мать, перетряхивать - перетрахивать, врёт - в рот. There are even examples where this "y" sound after a consonant is the only thing which distinguishes the words лёд - льёт. Лъя is by no means ля. I can say that french or German la will be really close. Why does no one pronounce french la as lya? Russians can hardly hear the difference between French L and Russian soft L. This as close as fs is close to th in English. Once again, there is a PHONEMIC distinction between a soft vowel and a vowel and a "y" in Russian. They are as different as v and w are for native English speakers, despite the fact that there are very few words which differ only by v and w.