Yes, the first time you launch LR6, it should find your LR3 catalog, make a copy and then upgrade the copy for use in LR6.
But the original catalog will be left intact and usable by Lightroom 3.
The question and answers here need a bit of clarification.
When you attempt to open the LR3 catalogs with LR6, LR6 will migrate your old data into a new catalog with a new format and new name. Your old LR3 catalog will be unharmed.
However, LR3 cannot read your LR6 catalog, and LR6 cannot use your LR3 catalog. Any updates to one catalog will never be seen in the other catalog.