It depends, if you are the average reloader that only uses loads found in a reloading manual, and your rifle and cartridge components match those used by the developers of the reloading manual, then no.
On the other hand, if you want to develop a precision load a combination of cartridge components not listed in any manual then yes, you need to use a chronograph.
Most people that reload are just that, reloaders, others are what I call hand loaders, they are the guys that will go where ever the testing points them. These are the people that need a chronograph. These guys will use any bullet, case, primer, and powder combination that produces the results that they are looking for, even if that component combination isn't listed in any manual...and that can cause problems that a chronograph can warn you about. A good example is the fact that most reloaders don't realize that bullets of the same weight and general shape from different manufacturers don't produce the same speeds or pressures. Using a Sierra load recommendation with Hornady bullets will most likely produce higher pressures and faster speeds than the Sierra manual lists. That wont mean much for most people because they are well within the range of safe loads, but if you might want to be aware of the difference in pressures and speeds if you are working on a 300 Win Mag for 1100 yard targets.
A chronograph will also help develop a bullet drop table that you can use as a basis for estimated bullet drops at various ranges. Without the chronograph you can't really know what the muzzle velocity is and you will only be guessing at how much drop you have a various ranges, that's real problem is you ever want to work on your medium to long range shooting skills.