It depends what theory you believe in. What are the best ways that I can describe these theories? Something that everyone can understand - examples from good old popular culture! These examples are always shrouded in fact anyway! There are three main theories that I can think of.
If you believe the first, which I will tentatively call the "Forever Young" approach, then yes, no matter how you bring the plant to the present, it will age considerably during the "trip" through time. (In some cases this might take mere seconds).
The second,is the H.G. Wells/ "Doctor Who" theory of time travel, where the plant is carried through time on some sort of vessel or ship. The ship, like a TARDIS, has a special interdimensional barrier which contains the temporal impact within it. Therefore when travelling through time, because the plant is technically within a different dimension, it stays exactly the same.
The third and final theory that I can think of is similar to the lines of "Red Dwarf" and its ideas on the parallel universe. Here the plant is taken fom time through a sideways shift. This may not be sideways in terms of time, just whatever the time zone that the dimension running parallel to us is at at the same moment. Therefore the plant doesn't change.
I'm sorry about the pop. references, I am just not very good at explaining things, particularly my ideas and understandings, that well! It's best to stick with the easy stuff!
Stay cool! I'll see you in the past!
Timelord