Absolutely without question yes. As a consultant it's even more important than for a full time employee. When you're consulting, up to date, deep knowledge = work. If there's stuff you don't know then that's potential work that you're losing out on.
Whether the knowledge is acquired by formal courses, books, conferences or just playing around depends, but the keeping up to date is not optional.
I pay for my own training, have for quite some years. When I worked for the bank I still bought my own books, bank paid for others and for exams. Now I pay for books, conferences and any other training material I need.
I'm doing my M.Sc, but that's not for work, that's because I want to study formally further than undergrad.
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability
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