Accepting donated equipment is absolutely ok, you are right, and as long as you have all the proper licensing to run the Server version, and the Terminal Services licenses, you should be ok... it is still a valid point that LANDesk would need to be Terminal-Services ready, which I believe it is. The biggest issue is that you would likely have to limit the usage of that model to web browsing only, any of the FHC licensed software (typically distributed through LANDesk or downloaded from the FHC site) will not be licensed for multi-session use. You could certainly put a call into support on that one, but it seems extremely unlikely. Once all is on the web, this would be a preferable model.. though as you've said, becomes an administrative burden..
Enterprise licensing agreements are typically not liberal as you've described, and are rarely in the form of use all you want for a single fee, they typically entail being able to install as often as you like, but each year at contract time your payment is dependent on your consumption during the year, or if you have agreed to a certain number, there is a premium to go over a given target, usually brought forward to the next contract. In the case of single application installs vs thin-client installs (Terminal Services), licensing is very different in both cases, and rarely are combined into a single agreement, they are different models at most vendors, and in most cases a whole different licensing team covers them. At least that has been my experience.
When you look at sites, many tools are advertised free to end users, I've been requested to put FREE stuff on servers regularly, when you investigate the licensing requirements with the vendor, it usually reads, you can install this freely, but if you make it available in a corporate environment on a server or through terminal services, there is a fee involved.
“A long habit of not thinking a thing wrong, gives it a superficial appearance of being right, and raises at first a formidable outcry in defense of custom.”
― Thomas Paine, Common Sense