Yes, it is entirely possible to have plants in the tank from the get go and it will actually help you cycle the tank. The plants will eat up nitrates when they appear in the cycle and I believe they may even help eat up some of the ammonia and nitrite which of course will make it safer in the tank for the fish. If I am not correct about the ammonia and the nitrite I am sure that someone will be along to correct me. I do know that the plants love nitrates though which is the by product of dangerous nitrites in the tank water.
Do you know about the cycling process in the fish tank? If not I believe there is a sticky on the top of the page with some great info. on the subject.Basically the whole process can take anywhere from 4-8 weeks weather or not you plan to cycle with fish or if you plan a fishless cycle. There are ways to speed up the cycle some such as using a filter that has been running on an established tank for some time or even just obtaining some gravel from an exsisting healthy tank placed in a media bag or an unused ladies nylon stocking placed in the aquarium under the filter intake or near an airstone so the water can pass through it. If there is space inside of the filter that is even better. You just leave it in the tank for a week or two and it will help jump start your cycle. It will help seed the new filter. After the week or two is up you can remove it from the filter. Of course you need to test the water during the whole cycling process so you can make sure the water peremeters stay in the safe range for your fish. Anything above .25 on the chart is dangerous and will require a small water change to bring the levels back into the safe range for the fish. I would suggest buying a liquid test kit to test your water during the cycle if you have not done so already. A good test kit is Aquarium Pharmaceuticals Freshwater liquid test kit. It is the best one on the market for freshwater systems. It will have everything in there that you need to test for including ammonia,nitrite,nitrate,ph, water hardness and possibly a few other things. Stay away from the test strips since the results tend to be rather inaccurate.
Also remember to add the fish slowly so you do not have outrageous reading in your tank water. Of course you need to add enough to start your cycle. What tetras are you thinking of adding to your aquarium? Some of them will withstand the cycling process better then others. Also, about the plants, what plants do you want to grow in your tank? What is your lighting like? I would start with some low light plants such as anubias, crypts,vals,java fern, and possibly java moss. They are easy to take care of and grow and do not require a lot of lighting.
By the way, welcome to aquaria central. You will find a lot of helpful people here waiting and willing to help you out in your underwater world.
Just some thoughts. Hope this helps.
Marinemom