No. For all the things that humans are really good at, picking totally random numbers is not one of them. There are certain numbers that people are more likely to consider "random" than others; for instance, odd numbers and prime numbers tend to be popular picks as far as "random-looking" numbers go, and this trend can make so-called "random" picks a lot less random that we'd like them to be.
To get a truly random sample, using a random number generator, especially a truly random number generator, will give you a truly random sample.
