Lighting a plant from beneath will cause the plant to grow towards the light, ergo, downwards, if it grows at all. Phototropism is the name of the process induced by lighting or sunlight from above - the plant wants to maximise the amount of light it receives, and therefore grows up towards the light. If you place the light to one side, the plant will virtually grow sideways; you can see this in the wild or even in a garden, where plants are perhaps covered by a dense canopy above, or planted much too close to a fence, and therefore produce growth that is reaching forward, almost sideways, groping towards the brightest area. I'm afraid your suggestion simply won't work in terms of growth, but if you want to use small leds at the base of plants for purely decorative reasons for short periods, that should be fine.
UPDATE IN RESPONSE TO COMMENTS:
I'm not going to reproduce a full botanical lecture here, but will add a little more info. Light is one of the most important things controlling plant growth; plants have a set of photo receptor proteins, four of which have been identified so far. Photosensors in particular detect the presence, strength, colour and direction of a light source, and that information is used to dictate direction of growth (phototropism), which is the most relevant for the question asked. There's also proteins called phototropins which are activated by the presence of uv/blue light wavelengths, and these too are involved in directional growth, although they're also involved in directing chloroplasts in order to maximise photosynthesis, plus one or two other twiddly bits. It's quite a complicated, synergistic picture, but simply put, your plants ain't gonna grow well without the proper wavelengths of light placed at an optimum distance above your plants. Simply put, you could view leaves as solar panels, angling their upper surfaces to catch the light they need.
In terms of whether light placed beneath 24/7 will affect plant growth, depends on the plant, frankly - some plants are more responsive to certain wavelengths of light, and many plants need some hours of darkness. And yes, it is logical to assume that the plant will grow towards the strongest source of light, provided that particular light gives the right wavelengths and spectrum.