Unlikely

The Artificer Battle Smith's Steel Defender feature says:

You determine the creature's appearance and whether it has two legs or four;...

At first glance, this might appear to offer you license to declare that the appearance of your Steel Defender is that of a 'hollow suit of armor', and specifically one that is perfectly sized for you to fit inside. However, this idea is quickly quashed by finishing the line:

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

Thus regardless of what you choose the appearance of youyour Steel Defender to be, it remains a size medium construct. Since you are a human (and size medium as well), so long as both you and the Defender are living creatures, you cannot willingly share the same space, which means you would not be able to "enter it" in order to find a "safe place for healing".

If you were size Small, perhaps some allowance might be made for creating a Defender specifically designed to provide you cover and obscurementobscurement, and arguably you could share its space by treating it as your mount. However, note that the Defender is supposed to be your faithful companion, and protect you by means of its Deflect Attack. No mention is made of you wearing it like armor. And for for Artificers who do specialize in making armor (that is, Armorers), their Guardian model at best produces a Defensive Field which grants you temporary hp, but nothing like a 'safe place' to retreat inside. If the Artificers that actually do make armor can'tdon't make such a thing, it does not seem reasonable to rule that a Battle Smith would be able to.

You might consider a dip in Warlock with a Genie patron if that"a safe place for healing" is what you are after.