Absolutely!
We humans have the tendency of giving character to objects, when a bond exists between the user and it's tool some form of characterization usually takes place, just think of the endless stories that exists of sailors and their ships throughout history. Mechs, specially in Japanese media do take center stage at the work( mainly for marketing purposes ) their design, name and other characteristics have to be distinct like the characters, however, that doesn't always happen and in some stories they are just simply another vehicle in the setting, were their "characterization" would come more from the world building of that story.
Of course, there are iterations where they are sentient by themselves, either being straight up lifeforms( the Cybertronians from Transformers ) or by having an advanced AI capable of thought ( BT-7274 from Titanfall ), which makes them not characterized objects, but straight up characters, being part of the cast or maybe, like in Transformers case, the main cast themselves. There also instances where sentience appears to them trough more "esoteric" means, in these kind of stories their sentience is hinted at, but not always explicit, it usually involves some Sci-Fi Technology or straight up Magic, although their characterization usually stays in a more "characterized object" stage rather than becoming a character, but there are some that become characters later on, like the Getter Robo and the Mazinger Z, both mechs have this Fictional energy source that somehow makes them evolve from a construct to a thinking entity.