I have a home built RepRap with all sides open..
Would there be any advantage to enclosing the print area in acrylic?
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It is hard to tell whether you personally should enclose your printer. However, you asked for the advantages and I will name some of them on which one can base a decision.
A 3D printer enclosure
There are obviously also downsides, as: connected work/money to make it, increased space used for the printer, and, if not well made for that purpose (which it should be), increased difficulty in repairs and maintenance of the printer itself (i.e. to get the printer out of the enclosure).
@kamuro provided an excellent answer, so I'll just try to add by playing devil's advocate.
Possible things to look out for:
People add a "passive heated chamber" when they are printing in ABS. However I personally think the best reason to have a custom chamber is so you can add an air filter. Adding an air filter will reduce your exposure to fine air particulates. It is generally considered a bad idea to breath in particles from plastic.
For PLA you will not want an air chamber. If you want to do an air scrubber they you will need air input to avoid the heat chamber from getting hot.
On that note as we see in the z18, PLA can benefit from an Active heat chamber, but you will have to figure out what the optimal temp is.