Yes. The Steel Defender provides cover.

RAW,

You determine the creature's appearance

and

...your choice has no effect on its game statistics

However, RAW, you can use other creatures as cover.

Walls, trees, creatures, and other obstacles can provide cover during combat, making a target more difficult to harm. A target can benefit from cover only when an attack or other effect originates on the opposite side of the cover.

And, there is precedent to gain total cover from inside of another creature e.g. being swallowed by a giant frog

... The swallowed target is blinded and restrained, it has total cover against attacks and other effects outside the frog

The total cover here comes at the cost of being blinded and restrained. So, you would have to work with your DM to determine what degree of cover is appropriate and at what cost.

The Rules explicitly state that being behind a creature can provide half cover.

There are three degrees of cover. If a target is behind multiple sources of cover, only the most protective degree of cover applies; the degrees aren't added together. For example, if a target is behind a creature that gives half cover and a tree trunk that gives three-quarters cover, the target has three-quarters cover.

Half cover provides +2 to AC, while three-quarters cover is +5.

Apparently, creatures always provide half cover

So, its feasible that a small creature could gain cover from its medium mount by building a chamber within it. And, maybe the chamber could even be structured to provide total cover.

The Steel Defender can provide cover.

RAW,

You determine the creature's appearance

and, while it's true that

...your choice has no effect on its game statistics

no game statistics need change for a Steel Defender to provide cover, since other creatures can provide cover.

Walls, trees, creatures, and other obstacles can provide cover during combat, making a target more difficult to harm. A target can benefit from cover only when an attack or other effect originates on the opposite side of the cover.

A creature, like the Steel Defender, can provide at least half cover.

There are three degrees of cover. If a target is behind multiple sources of cover, only the most protective degree of cover applies; the degrees aren't added together. For example, if a target is behind a creature that gives half cover and a tree trunk that gives three-quarters cover, the target has three-quarters cover.

Half cover provides +2 to AC, while three-quarters cover is +5.

Now, the Steel Defender is a Medium sized creature, and cannot share the same space as another Medium creature. So, it could not serve as a suit of armor for a Medium or larger creature. But, it can share that space with a Small or Tiny creature. And, it can even serve as that creature's mount.

It's perfectly feasible, then, that a player could decide that appearance of a Steel Defender includes a Small chamber that could accommodate part--or even all--of a Small creature.

There is precedent to gain total cover from being inside of another, larger creature, e.g. being swallowed by a Giant Frog.

The frog makes one bite attack against a Small or smaller target it is grappling. ... The swallowed target is blinded and restrained, it has total cover against attacks and other effects outside the frog

The total cover here comes at the cost of being blinded and restrained. Moreover, the frog can only Swallow creatures smaller than itself. So, you would have to work with your DM to determine what degree of cover is appropriate for your PC, and at what cost.

So, yes, its feasible that a Small creature, at least, could gain cover from its Medium Steel Defender Mount by constructing a chamber within it. And, maybe the chamber could even be structured to provide total cover, if you have a generous DM.