I'm on my ipad round the pool in Cyprus at the moment answering this, how sad am I? actually scratch that- it's the perfect place to be!
No, most designers won't insist you have a web design done at the same time. If they're pushy like that- bin them.
And it shouldnt be a problem at all to add a logo design to a website at a later date.
Back to the rain in the morning :Scared:
p.s. Thanks for the nice comments guys
p.p.s Be careful with some of the "free" logo maker sites out there. For example the one listed earlier will give you a template based logo, which wont be unique, thst you can use on the web. But if you want to use the logo in print (like on a business card) you have to pay £49 for a high resolution version.