No, those restrictions still apply. It's the proficiencies that aren't affected. The skills and casting still are affected by the armor.

For example, with my FTR/Druid. A druid can't wear full plate. But when I dual classed from FTR and my Druid level became a level higher than my FTR level, she was able to wear full plate (Druid spells are divine, so aren't affected by wearing armor). A dualled FTR/mage is still restricted by the armor when it comes to casting spells. That isn't affected. But, he could wear armor if he wanted, whereas a pure mage can't even put the armor on.