Believe me it does. I used to work for Sun Microsystems for 14 years in Solaris support and sustaining and I can guarantee you that it does.
You problem is that Solaris has concept of Secure Runtime Linker, and for trusted applications most of LD_CONFIG and LD_LIBRARY_PATH is ignored for security reasons.
For secure applications LD_LIBRARY_PATH components are ignored for non-secure directories.
Your dovecot is probably setuid or setgid and considered as secure application and secure runtime linker rules are triggered for it. Then /usr/local is completely ignored from LD_LIBRARY_PATH.
Sami