Is a melee-centric party without a healer viable in Dragon Quest IX?

Against the different boss, heavy healing is necessary. Starting with the third or so boss, he will hit twice per round, often with multiple target spells (megastorm or something like that in english, for example), so heavy healing is needed. Plus, some can heal themselves, drawing the battle in length. A dedicated healer is, in my humble opinion, necessary. Even with a priest dedicated to healing, I am sometimes constrained to use the healing spells of the main character to keep the whole group alive.

Unless you manage to have a damage output of hundreds of damage per round, you won't be able to kill a boss before he kills you.

Edit : Sometimes use of buffs/debuffs is mandatory. You won't survive a heavy hit with an alteration on your party and you won't damage a boss with protection on him, thus, you must counter those spell with the appropriate buffs/debuffs, and a buffing/debuffing player does not deal damages. Likewise, you have to counter alterations effects (sleep, paralyze, etc.). Also, the time a member of your party is healing himself or another one, he doesn't do damages. Having completed DQ4 and 5, and seeing DQ9 is the same and even harder, I can tell you cannot survive without proper healing.

The healer is quite useless on random monsters encountered on the map. My personal advice : specialize your healer in magic wands, this way you can regen the MP of your healer on the random encounters to arrive fully charged against the boss.

It's absolutely viable, but it's entirely likely to require more grinding. You'll likely have an easier time dealing with random encounters, and a tougher time with bosses.