It is very important. The semantic difference would be even bigger than that in English between "Overthrow" and "throw over. Basically, placing the prefix the wrong way you are using the wrong word, which sometimes doesn't even exist - as is the case with "vorstellen", that only exists as a separable verb: https://www.collinsdictionary.com/dictionary/german-english/vorstellen
Another good comparison would be "set up" and "upset".
To bring a German example off the top of my head, we have übersEtzen (with the stress on the words root) that means "translate" and we have Übersetzen with the stress on the prefix, that means to ferry somebody from one bank of a river to another.
The grammatic topic you may want to look into is "separable verbs in German".