Based on what I know - No.
It means that you have two CPUs that can help you to process jobs
"simultaneously" but doesn't mean it will double its power.
CPU is like a machine in a production environment and they actually use
manufacturing theories and algorithms for CPU design.
So instead of you have one powerful machine, you now have two
maybe_not_so_powerful machines.
But you may ask, why will it be good? Because many jobs don't have to wait
and can be processed by two machines at the same time, instead of one which
will delay other jobs that could be finished earlier. This is so-called
"parallel processing" in production.
Example: One processor is handling virus scanning and the other one is
handing the rest of jobs from the user and applications.
Now, here is the tricky part. Image you are the foreman and you are
responsible for assigning jobs to the two (or more) machines; what things
will you consider?
That's the challenge for OS and applications, and in this case, they are the
foreman, and they have to constantly "re-schedule" and "re-dispatch" jobs
based on inputs from user, devices, and program instruction sets with all
kinds of constraints.
In addition, processors also have to do their parts once they have received
the jobs.
So in theory, we should have more throughputs (which transfers to what we
call performance or "fast") but the result really depends on the quality of
job scheduling algorithms in addition to processing speed.
There are other cosniderations for why CPU went to multi-cores instead of
higher clock, but let's forget about that for now.
Mt 2 cents, and hope someone could also share if I am wrong.