In 44 years of practice of the engineering profession, having taken part in dozens of engineering projects, some of them small and other quite huge, having worked with dozens of engineering companies, some of them almost unknown and others which were famous all over the world, I've seen both procedures, i.e., sometimes the welding details were drawn and sometimes were indicated by the AWS symbols.
In my particular opinion, good engineering practice recommends to use the AWS symbols, so there won't be any wrong interpretation.
Giovanni S. Crisi
Sao Paulo - Brazil
AWS welding symbols will usually do the trick in 95% of the cases. However, use a sketch if a standard welding symbol does fit your needs. Don't make up welding symbols to describe conditions that aren't addressed by A2.4. For example; a partial circle located at the apex of the leader and reference line should not be used to specify a weld that is "nearly" all around. The weld is all around or it isn't.
I've run into many "designer" welding symbols that only confuse the welder and supporting staff.
Al