Yes , generally if you check email on the desktop and no new ones have arrived nothing will show up for the laptop to receive.
You can test it by sending an email from the desktop to yourself and then check for it on the laptop.

You can change a setting so the message stays on the email server for x days or such , so you can get the messages more than once , or on other computers. If you want to set it up that way let me know and I can help you with that. but you will tend to get duplicates if you check on both machines frequently.

here's the basic "how to" set up OE -
http://www.microsoft.com/windows/ie/.../oe/setup.mspx
you must have that right since you have gotten an email now.

next thing is you should export/back up your desktop address book as a file so you can email it to the laptop. Just send it to your self and only check for it on the laptop.

or you can connect the 2 machines and copy the file over that way.
or if you have a flash drive or cd etc
- copy the address book to one of those and then add it to the laptop.
then use the laptop OE address book to import into the OE.

It may be the default set up in OE to send email addys not in the address book to the spam or junk folder. not sure on that.

I use Thunderbird email program but in some ways they are similar. It's been quite awhile since I installed and used OE to test something..

Do you have multiple email addresses for yourself ?
are they all added into the OE on the laptop?

basically, except for any special buttons, a laptop should work the same as a desktop.
Do you have the same OS {operating system}one both machines?
like windows XP or Vista?
Or is one XP and one Vista?


For me {a XP user with classic/customized appearance} Vista takes a little getting used to, just because how it looks, of extra click to OK stuff, and usually someone else's computer that I am helping them with -so it isn't set up like I prefer.