If I were to have a fire, I would not leave it out in the rain. Whether I attempted to have a fire in the first place would depend on a number of factors; availability of fuel, length of day remaining, how cold/wet I had become and what clothing and sleep gear I had.
If I had a fire, I would want to be able to squat near it to tend it and benefit from the heat without being sat out in direct rain. If everything is wet, and its cold, a small fire is likely to need all the help it can get to give off useful heat. If the tarp is so far from the fire that it can't shelter it, the fire isn't going to do much to heat the area under the tarp. If it is raining and the fire isn't sheltered, you won't be able to dry anything stood in the rain next to the fire.
If the light is failing and fuel isn't lying around in abundance, you can get into more difficulties stomping around trying to find fuel, then trying to get a fire going, than you would if you just battened down the hatches and stripped off wet gear and got into your sleeping kit, cooked on a little stove and got hot food into you.
I remember a story of a chap who overturned his canoe in Canada, bitter weather. He got himself out but knew he had just minutes before he would become too cold to function. He set fire to one of the massive log jams piled up on the side of the river, stripped naked and roasted alternate sides of himself while drying his clothes next to the roaring inferno. Lots of fuel, very wet, very cold, no dry gear to fall back on.