Will Windows XP Pro use both Pentium II processors in a dual processor
machine? (Note it is a Pentium II I'm talking about.)

Windows Xp pro will able to use dual processors but you also have to
use appications that takes advantage of that. Appication like Adobe
photoshop would able to utilize both processors

But will the XP operating system and it's programs (like internet
explorer) operate faster will 2 PII processors installed instead of 1?

In theory, yes. XP could run system processes on one processor, and
offload the iexplore.exe (why are you using Internet Explorer,
anyway?) process onto the other processor, meaning that the first
processor has full attention for XP alone. However, I've never used an
SMP system enough to tell whether it'd do this properly, and I'm not
so sure that it would be that much faster.

If you're running a multithreaded app (one designed for multiple
processors), it'll take advantage of it. If you're running multiple
apps (for example, Photoshop and Word, or something like that), it'll
take advantage of it. A single, non-multithreaded app? It might be a
little faster.

You will get a speedup from having two processors active in the
system. If you're using only one program at a time, XP will tend to
schedule its own activities on one cpu and use the second cpu for the
program you're running.

What you won't see is a 2x speedup of everything. Programs have to be
written specifically for multi-cpu use to able to use them. As well,
you may have two cpus, but you've only got one set of memory, and the
two cpus will be fighting for access time to the ram.

Thanks for the comments. I guess my purpose was to pick up a second
PII processor (they're giving them away on ebay) for some of my old
IBM Intellistations that have 2nd Type 1 sockets, if the system might
overall gain a little noticable speed. (I know about multi-threaded
aware programs, like Photoshop. I was just thinking of the general
operation of the machine, loading files, maybe a little faster display
of internet pages with a second processor.)

Additioanl comments/thoughts are welcome.

Yes, XP Pro will make use of the second processor *provided* the
processors meet the minimum recommended spec for running XP. Unlike XP
Home which can handle only virtual second processors (as in
hyperthreaded CPUs) XP Pro can handle up to two processors (not more).
However, what you need to find out is whether the CPUs fall within the
minimum specs; I couldn't find info on that at the Microsoft site. The
below page doesn't seem to provide a link to the info:
http://www.microsoft.com/technet/prodtechnol/winxppro/evaluate/default.mspx

There is this third party page answering general questions on dual
processor systems:
http://www.bestpricecomputers.ltd.uk/ent/dual_processors.htm