Yes, the present can be used instead of the future, but a time specification must be present:
Vado a prendere la macchina nuova
Domani vado a prendere la macchina nuova
In the first case, without time specifications, the speaker is going to get the new car now. It can also be
Sto per andare a prendere la macchina nuova
if the action will take place in a short time. All action verbs can be used in the same way:
Telefono a Maria (now)
Domani telefono a Maria (tomorrow)
Il mese prossimo telefono a Maria (next month)
The future need not be immediate, as the last example shows; even
L'anno prossimo vado in vacanza a Forlimpopoli
would be good. Similarly,
Corro a prenderlo (now)
Fra un anno corro a prenderlo (irony implied)
The verb “andare”, though, has come under the sad fate of being used for “immediate action”, particularly in the fashionable jargon of TV programs on cooking:
vado a infornare, vado a impiattare, vado a versare
where the speaker moves not farther than a few centimeters. Avoid it, if you're not a wannabe chef.