Yes they will, they start on Sat 28 May and run at the same times as last year from Great Yarmouth (1040 and 1310) but slightly differently from Liverpool Street (1000 and 1230 (used to be 1200)), the latter taking nearly 3 hours to get there!
Looking at nationalrail.co.uk, it's quicker to take the 1230 from Liverpool St and change at Norwich, arriving 1509 as opposed to 1528 by staying on the direct train. I noticed that, last year, the departures boards at Liverpool Street didn't show the Yarmouth trains at all (under Great Yarmouth, that is). The Saturday services were all shown as connections, with no mention of the two direct trains.