Can I grow like this?

Surge protector inside your tent with only the extension cord and grow light power cord coming out of your tent. Other than that you'll have to put your socket inside your tent

 

A lot depends on what lights you have and how many things you’re plugging in and how much space you have. Do you know what kind of lights you’ll be using? If you have lights with a driver I highly recommend putting it outside of your tent.

 

Closet of your bedroom or another room in the house?

When I grew in my closet downstairs, in a spare bedroom that was used for storage and misc stuff, I just ran an extension cord from the nearest outlet, under the closet door and into the closet, plugged in a protected power bar and mounted it a few inches off the floor on the corner of a wall. Plugged in timer and light from there, fans in there, kept all the wires on the one corner, off the floor and away from water. No carbon filter but the inline fan was mounted at the top, and I ran some duct from that and out the cracked door of the closet. Room was dark so I didn't have to worry about light leaks.

Putting a tent in the closet would help even more, remove the worry about light leaks, and dampen the noise from fans a bit more.

 

You realize that you have to move a lot of air, and that makes noise no matter what. I think the minimum you want is to exchange all the air in your tent at least twice a minute. Also that air has to go somewhere. If filtered the smell might be ok, until you open the tent. You will be checking it daily at least.

 

dude, anything is possible

aka. stealth grow.

let us know how much space u r working with and we will recommend a light.