Once again - I defer to newmomm - her answer provides more information and rings totally true. That is what I SHOULD have said. Sometimes it is easy to assume we define things the same, but we may not. But I hold my child, read to him, and have quality time together in such a way that he knows I am Mommy.
@southernmd: you answered according to what "in a meaningful way" means to you, which is totally fair! And much appreciated - I was a little shocked to see the first answer to this question, I have to admit.
To the OP: In addition to what you mean by "meaningful", it also depends on you and what, exactly, you're trying to do. Graduate top of your class and train as a neurosurgeon? Whole different ball game than put in a solid performance, potentially stretch things out a little when you're able, and go into a more primary care -ish field. Furthermore: can you afford not to work while you are in school, and to pay someone to do all non-essentials so what time you do have is all with your kids? Or are you going to try to be shopping sales and scrubbing your own toilets as you go? It comes down to these details, I think....
I guess it depends on what you mean. You won't finish training until your toddlers are teenagers, so there probably will be some stuff you will miss. You are going to miss out on some dance recitals, sporting events, Christmases, and birthdays. You may not get to know all of their best friends and secrets and be room mom. Or if you do, it will be planned in advanced, a little rushed, and you will be kind of exhausted.
However, you can certainly still have a meaningful relationship with your kids, read them stories, talk about their day, sing songs, and be a great role model in their lives.