No, if truly random it could be any number from 0 to infinity. The randomization doesn’t impart any qualities to the selected number.
If you randomly selected numbers from the infinite range of numbers for an infinite number of time, you would get a result of “7” just as often as getting “3.456e11”.
The probability of getting a finite number is pretty much zero.
For any range [0; n], where n is finite, there are always infinitely many numbers larger than n, so the probability of getting a number in said range is n/(n+infinity). I feel very confident in saying that something with that probability will never happen.