Long Rest - One per Day.
The question was restated to articulate you didn't mean long resting all day, but I will leave this here for other searches.
The rules for a long rest state that you can only benifit once per day. That means that while you don't need to sleep you still can only long rest once.
A character can't benefit from more than one long rest in a 24-hour period, and a character must have at least 1 hit point at the start of the rest to gain its benefits.
Short Rests - Yes, But Why?
I suppose, as long as you only do "light activity" which is defined as:
nothing more strenuous than eating, drinking, reading, and tending to wounds
you could spend the downtime chilling in bed -- binge watching the midevil fantasy world equivalent of NetFlix, or reading. But, what does that get you?
A character can spend one or more Hit Dice at the end of a short rest, up to the character's maximum number of Hit Dice, which is equal to the character's level. For each Hit Die spent in this way, the player rolls the die and adds the character's Constitution modifier to it. The character regains hit points equal to the total (minimum of 0). The player can decide to spend an additional Hit Die after each roll. A character regains some spent Hit Dice upon finishing a long rest, as explained below.
After the hit dice are spent, or you're at max health, and spell slots replenished, what is to be gained? You could cast all your spells, and begin resting again I suppose.
The DM Can Stop You
The DM has final say at everything at the table. They can say, "Your rest is interupted by a noisy person in the room next door," or simply "No." The DM might see this kind of hack as an abuse of the rules, and can either amend or ignore the rule to keep balance at the table.