We did just that. Though we treat our wireframes as a guide and not as a set in stone layout. It can save some money, but it really helps the group responsible for the web site to discuss what content is needed before the design starts.
I've been on both sides of this and as a designer I was always frustrated when I wasn't included from the beginning. It was common for me, as a designer, to find problems with the wieframes because the programmers, content experts, etc. didn't have the designer eye/expertise. I always include designers as early as possible in the process.
I would not say it is advisable even given resource limitations, but it is not an uncommon practice. I completely agree with David that it can be frustrating to the designer. I would advise involving the design team as early as possible. With so much importance placed on web sites as a marketing tool, can you really afford to skimp on the online brand of your institution?
Any good designer will do the needed due diligence to create a great design. With wireframes and research provided to the designer, they should get up the learning curve much faster. If they see a problem with the wireframes and/or content, they should have the liberty to point out the problem and suggest solutions. As I stated earlier, use the the wireframes as a point of discussion and a straw man to get the stake holders in agreement before you engage a designer.
Designer that get frustrated over the process, feedback, and decisions are very difficult to deal with. I suggest vetting your options for a designer before you engage one. Find one that is emotionally mature, has a proven track record, and that has a designed an aesthetic similar to your desired look.
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