I was thinking, would your arms lag in the beginning if you do not do direct arm work?
Reason I say this is that the other movements in your compound exercises will be the weakest link in the beginning. For example, if your doing benchpress your shoulders would be the weakest link in that movement and until your shoulders get stronger you will not be working your tricept mucles and chest muscles enough to get any serious gains.
Think any other exercises, like pullups, maybe your bicep will not be worked effectively until your lat muscles get to a certain point and your bicep starts to become the weakest link.
It makes sense because there must be different stresses on the different mucles in the beginning of working out until everything gets evened out.
I've noticed this because I stopped doing Barbell Curls for 3 months, while I was doing pulldowns my strength incresed hugely in that exercise. But when I went to do barbell curls again I could barely do the same weight I did 3 months ago.