According to an empirical study by Christopher Trudeau, the answer is yes. I think his 2012 article deserves greater attention–The Public Speaks: An Empirical Study of Legal Communication, 14 The Scribes Journal of Legal Writing 121 (2012) (here).
In a carefully designed study, subjects compared passages written in plain English and similar passages that contained the failures that plain English attempts to eliminate. The study provides a good bit of valuable information. It also results in 10 practical pointers.
First, do not underestimate the importance of oral communication. Over half of all respondents preferred some type of oral communication to written communication.
Second, deliver written documents electronically even when you must send a hard copy.
Third, use clear, understandable written communication.
Fourth, do not assume that all readers will understand commonly used legal terms. Instead, define these terms if you must use them.
Fifth, avoid complicated terms and Latin words. They generally bothered or annoyed nearly seven out of ten clients.
Sixth, prefer the active voice. Respondents preferred it almost 70% of the time — and clients at a higher rate than non-clients.
Seventh, avoid multi-word prepositions like pursuant to and prior to and with regard to. They are among the worst aspects of legalese.
Eighth, remember that the more confusing the sentences become, the more likely that a reader will prefer plain language.
Ninth — and this needs to be proclaimed repeatedly, ceaselessly— the vast majority of clients and non-clients prefer plain language. For the choice-of-language questions, readers chose the plain-language version 80% of the time.
Finally, use plain language no matter what the reader’s educational level. Contrary to my original theory, as the level increased, so did the respondent’s preference for plain language.