Yes, it just has a couple of "forks" holding it in, squeeze them together and it should just pull out.
If you have a manual trans, i.e. no trans cooler, the rad can be pulled out fairly easy, just two bolts at the top, maybe 4 if shroud has bolts not clips.
Shroud and rad just have tabs/pegs at the bottom so lift out once top fasteners are released.
That's if you want to back flush the rad, i.e. flip it sideways to run water in the "lower outlet"(top now) to the "upper outlet"(bottom now), this will push out any larger debris that may have gotten stuck in normal top to bottom flow.
You can also lay rad flat and fill it with warm water/CLR mix, let it sit for 20min. then flush, repeat as you see fit.
Heater core is also good to back flush, it can be done just using garden hose.