Not without pulling hard on the inner door, which I only saw worked when another cyclist did it. Like you I like to keep an eye on my bike and at a previous stop I tried to open the door, but there wasn't a button to press, so thought you needed a key (which the guard uses, he doesn't force the door).
As I recall there isn't an auto button like on the doors between carriages - just a "handle" * which you pull sideways.
* technical term.
The door isn't locked - just pull it normally - no need for special tricks, breaking and entering tools, battering rams, keys, cutting equipment.
So I'd check your bike now and again if you want - or when you can see through the window that another cyclist is getting on.
As for getting your bike off through the outer door, just tell the train manager/captain or whatever they call him - he's often to be found in a mini office/cupboard.
They used to reserve a special seat for cyclists near the bike compartment but this may have changed with covid.
I usually find them very well organised if you communicate wit them - last time I got on (at Preston) the guy helping me get on knew that three bikes that had come down from glasgow were due to get off so he cautioned me to let them off first.