OK == for my example Im going to use myself. What happens when you do not provide enough nutrients to the plants in the form of dosing.

Say one such as myself sets up an Aquarium with a good amount of light to be considered medium-high lighting. They have pressurized CO2 and keep it to a safe level for the fish. They feed their fish apropriate amounts, sometimes a little extra. They give basic fertalizers such as seachem root tabs, seachem flourish, and seachem flourish trace. But they know that the tank would be lacking in some respect of some nutrients.

Would this promote algae or would it deter algae? What do you do if you just dont want to mess with fertalizers and doing 50%+ water changes weekly?

In my experience and in theory, yes. Once the plants are starved for something, anything except for light, the algae will take over and use what IS there.
The aforementioned person DOES have fertilizers, so if they don't want to "mess with" them, they just won't be dosign them? And even if they do, a 50% pwc every week is not necessary, unless "they" are dumping stuff in.

I would suggest that this person whom none of us know use the fertlizers they have, and start small. With a close watch, they will start to see different deficiencies arise and different types of algae come in to play. Once this happens, they can
1) start dosing the appropriate ferts (according to deficiencies/algae)
2) get lower lighting to slow down ALL growth
3) get TONS of algae eaters and hope
4) watch the algea proliferate

As I understand algae, and that isn't very well, we need to make sure there is enough of everything the plants need, plus a little more, other than light intensity. For a given amount of light, the plants need a given amount of fertilizer and CO2 (a fertilizer too) for every day's growth. If we let even one of those needs be unsatisfied, algae may take the opportunity that provides to begin to grow. The only exception seems to be ammonia. Plants can use ammonia for nitrogen, but a sudden increase in ammonia takes awhile for the plants to get started using it, while the simpler organism, which is algae, can start using it right away, and it has evolved to do so - the algae spores begin to "hatch" the moment the surge in ammonia occurs. Have I oversimplified???