Yes, aphids (along with other sucking insects) can transmit viral diseases such as Mosaic virus, but if you can't tell whether the plants are 'ruined' then my guess would be they're not!

Why give up on them until you see signs of disease?

Just keep going with the aphid control. As far as the ants go, they may utilise the honeydew the aphids produce, but they don't go out and find new aphids and carry them into your garden, so if it was me I would focus on the aphids, not the ants.

If I had serious aphid problems I would also start thinking for next year about why the aphid infestation is so bad. Doesn't help you now, but could make gardening next year a whole lot more relaxing if you could change conditions so things don't get so bad again.

pepper,

I'd escalate to Sevin right away. Neem Oil is more of a preventative in their early stages. Once they really establish colonies you need to hit them hard. I am dealing with even tougher Psyllids and they just laugh at Sevin. I've hit them with a very dilute solution of Permethrin, but I won't eat the fruit with the overspray. At least, some of my plants not sprayed with Permethrin should survive producing tomatoes. Next Season, I plan to get a jump on them very early in the Season.

Raybo

Sevin will just bring in more problems. It will kill any beneficials you have. That is why Raybo still and will always have problems if the chemical use continues. The problem is that your plants are not healthy enough to ward off these evil creatures. Most pests attack sickly plants before they would a healthy plant. What are you using for fertilizer? What have you done to your soil to get it ready for your plants? Does your soil drain well and does it hold moisture? I know that last question will sound stupid to some but healthy soil will both drain excess water and hold moisture. Lots of organic material will accomplish this. DE will help control the ants. Apply it liberally to the soil surface and reapply after rain but don't look for instant results as it takes a few days to wear their joints. Greenlight brand 70% neem oil kills aphids in a few minutes if not instantly. It smothers the ones directly sprayed. Spray in the evening for the best results and make sure to get the undersides of the leaves. If the ant nest is a few feet away from your garden you can use something more potent but if the nest is in your garden then using something stronger will also kill any pest predators and possibly contaminate your veggies.

The problem is that the ants protect the aphids against predators. I had success using neem but I did NOT spray it on the plants. I sprayed the ground under the plants. Ants avoid neem oil so they were unable to cross it to climb the plant stems and "farm" the aphids. Natural predators were then free to take care of the aphids without ants driving them off.

I haven't seen an aphid all year - knock on wood.

I have lots of stuff flowering - kale, oregano, bee balm, sweet peas, etc. I wonder if this drew in a lot of beneficial?