Yes, you can put plants in an uncycled tank. Many people think that this is the most natural way to cycle a tank. It does require patience however. I just set up a quarantine tank that way. If I'd been in a rush I would have used ammonia and cycled it in 10 days or so. But I loaded it up with fast growing, "nutrient eating" plants and let them establish themselves for a few weeks.
I also took the sponge that I was going to use in the new tank's filter and sat it in one of the filters in my established tanks for a couple of weeks before I even set up the new tank, so that it could load up on "nutrifying bacteria". Then used it in the new, uncycled tank's filter. Doing that gives you big head start to-wards a cycled tank.
About 2 weeks after I had it stuffed with plants and running one of my angels looked a little funny and I wanted to isolate him and stuck him into the new tank, and he was fine, and in fact, I'm sure helped finish the cycling process.
So if you have the patience and the money, pick up a bunch of nutrient loving, fast growing plants. Buy as many as you can and stuff them in there. One good thing.....the plants you'll use are some of the least expensive ones to buy.
One last thing. You will be running about 3 watts/gal. with that lighting, so IMO, you definitely will need at least a couple of bottles of CO2 running to help get the plants going quicker, or you stand a good chance of having an algae problem. Newly set up tanks are prone to algae blooms until the plants establish themselves.
Len