The short answer is no, but with a caveat. The more complicated answer is it depends. Much depends on you, your skill, the area in which you are likely to find yourself, and your mental attitude, and what type of situation you find yourself in.
A cheap sleeping bag is nothing more than a blanket with a zipper attached and is made from various materials, and usually, weighs more than three pounds. Take that three pounds and add another three or four pounds for a tent and sleeping mat and you are headed for a heavy pack. Therefore, if you can only afford a cheap sleeping bag, then you may be better off leaving it behind. However, if you are willing to spend upwards of 400 dollars or more for a quality, lightweight bag and one that can be compressed to reduce volume in your pack, then the answer is yes.
Lightweight is less than two pounds and can be rolled tight so it takes up less space, and yet provides warmth. How much warmth is needed? Well for areas that essentially have a fall, winter, and spring then one rated for 20˚ F is probably adequate. For sub-zero temperatures, you will have to step up and pay more, and of course, this may add considerably more weight.
Sleeping bags filled with Down versus synthetic fills are lighter and more compressible, which means they can be rolled tight to reduce volume and they weigh less. Down filled bags will have to be dried properly if they become wet and some people find the Down filler can become displaced.
A 100 percent wool blanket can weigh five pounds or more and they are hard to roll tight to reduce volume. If your camp is stationary and have a way of transporting supplies other than on your back then wool blankets are an excellent choice and some would prefer one to a sleeping bag. Your sleeping platform should be raised off the ground regardless of the ambient air temperature.
If you find yourself in an escape and evasion situation, or one where you may have to defend your camp then a sleeping bag is not ideal, nor is a tent for that matter. A quality sleeping bag is typically mummy shaped, and so, your movements once inside are restricted. After all, in an ideal situation, you will not have to sleep with a pistol or rifle in your hands, but if you do, do you want to be snuggled tight in a bag. The decision to carry a bag is up to you, but carefully consider where you will be traveling and what will you be doing or might possibly be doing.
As we stated before a cheap bag is nothing more than a cheap blanket with zippers, and will be heavier than it needs to be.
If you have the skills, you can put together a sleeping platform using what is available and with a tarp and a bivy sack or shelter, you can sleep warm.
Leaves, dried grasses and/or dry pine needles can provide good insulation when wrapped in a tarp. Simply fold the tarp over after piling the vegetation on one side. Dried grasses, leaves and dried pine needles are ideal. Green vegetation, however, is not ideal because green vegetation will release its moisture to be absorbed by your body. The evaporative process will cool the tarp and other insulation, which is the opposite of what you want to happen.
Solar blankets are another option. Wrap in one and use others to reflect the heat of a fire into your shelter, or reflect the heat against a backdrop of dry rocks. Camp up close to a rock outcropping and build the fire so it reflects against the stone.
Ground insulation is important. Your body’s heat will conduct away from you into the cooler ground if not properly insulated. Warm always conducts to cold. You want the heat your body generates to stay put.