Will a 2006 era computer with a pentium dualcore and 3gb of ddr2 bottleneck an r9 380 for mining any type of altcoin?
It depends on the coin's algo and its requirements. Some algos are memory bound meaning they require more
memory than the GPU has available and it has to start transferring large amounts of data back and forth between
the CPU & GPU.
On the CPU side you should only run into problems if you have a multi card rig with a small CPU. I like the CPU to
have as many cores as miner threads (one thread per GPU card) and, at least, as much memory as the total of all the GPUs.
In your case if your GPU has 3 GB of memory, or more, you could have a problem.