Aphids feed on plants by inserting their mouth parts into the flowing juices within the leaf tissue. They seem to greatly prefer young leaf (suckers and the newly growing leaves), over more mature leaf. Research has shown that they are sensitive to the nicotine levels, which probably explains their preference for younger leaf. When sucking aphids are forcefully rinsed away with water, it damages their barbed mouth parts. (But, this requires hauling out a hose, and spending as much as a minute per plant, to get the job done. And it needs to be repeated every 5 to 7 days. It's nearly impossible to adequately hose very tall tobacco.)
A relatively small number of aphids don't seem to cause noticeable harm to the leaf, but a heavy infestation retards leaf growth. The honeydew (oh so sweet aphid poop) will attract ants, which don't harm the leaf or the plant. As the honeydew dries on the leaf, it remains sticky, and oxidizes to black. During prolonged humid conditions in the shed, leaf with substantial honeydew is more prone to developing mold (due to the presence of richer food for fungus growth). Kilning the leaf does allow the dead aphids to be easily brushed off. Sometimes there is a residual stickiness near the base of the leaf, but this is usually trimmed away from wrapper. I haven't noticed any effect of residual honeydew on the taste of filler.
I try hard to reduce the aphid burden early in the season--using detergent water, in order to allow the plants to grow well. Late in the season, I just have to let them have their way, if they persist. The detergent rinses away in rain, and oxidizes to nothing on the underside of leaves, but I don't trust it to be completely gone if I spray within a couple of weeks of harvesting the leaf.
Systemic poisons, like Admire (imidacloprid) are a threat to honeybees. This is particularly so if sprayed in the field. When used in seedling water, the risk is greatly reduced, though there is still some effect on pollinators that visit the maturing plants. So, if you are inclined to use a systemic, I would limit it to application in the seedling water.
Another poison approach is to spray "food-safe" permethrin onto heavy infestations, allowing several weeks before harvest. It kills most insects (good or bad) while it is active. My own use of permethrin is limited to a single spraying of the bud head of seed-producing plants immediately before bagging them. This zaps any aphids, and avoids seed pod damage from budworms and other pests that might destroy the seed. I only do this when there is little to no breeze that might disperse the spray beyond its intended target.
Bob