that's a relief
not having the full power available can cause all kinds of issues. most extreme and most often seen is that it simply won't power up and keep the pc itself from powering.
does not sound like the case for you so you'll most likely see the card throttling due to not enough power or even have random issues with it just shutting down when heavily used.
in the end you should be sure your card is fully connected and fully powered to get the full use of it. no reason to spend so much on a nice high end and then not give it the power it needs to excel.
be kind of like buying a $500k Ferrari and refusing to put premium gas in it :/