If by synergy you mean the one between melee skill and str/dex bonus then yes, it's your effective skill that matters for this calculation.
Just like evasion, dodge is not simply a chance to avoid being hit. It's a skill which is put against attackers weapon skill to determine the hit chance.
The 60% cap that you probably mean is reached when your dodge skill is twice the attackers melee skill. Some enemies have very high melee skill. One example would be the arena champion which probably has 300+ in melee. So in order to "cap" him out you would need 600+ skill in dodge which is impossible to achieve, even with 18 agility, Nimble, Evasion and highest quality infused syphoner leather armor and tabis. But guys like him are the exception.
I don't know how much melee skill most of late game enemies have by my guess is somewhere around 200, so in order to cap them out you'd need 400+ in dodge which can be achieved but only with at least 10 agility, Nimble, Deflection and good quality infused leather, but you don't really need that much to dominate. Being around 220-240 dodge at level 22/23/24 is pretty solid.
To get back to your question, if you leave your dodge skill at 0, Deflection will raise it to 60 which is as good as nothing. Only the lowliest of critters like rathounds will have their melee skill less then 50% of your 60 dodge in order for you to "cap tem out".
High skill enemies will hit you anyways. If your dodge is the same as enemies melee than the chance to get hit is 70% (base precision).
It may not be a matter of all or nothing when it comes to dodge but at the character creation you have to decide to either focus on it and get it as high as possible (agilty, +dodge gear, low armor penalty, Nimble) or completely dump it and rely on your ability to soak up damage (metal armor, alot of hitpoints, additional non-armor damage resistance (Conditioning/Stoicism feat + lifting belt + mushroom brew + morphine shot), Guard feat (good for str builds).
One way of keeping dodge low and still being able to somewhat avoid being hit is the Uncanny Doge feat which makes 3 melee attacks automatically miss plus an additional attack for each 30 points in dodge, but yeah you see it's also more effective if you have high dodge.
Maximising evasion on other hand is always usefull (unless your armor penalty is really high) because even when it doesn't help much for evading bullets it still reduces AoE damage (grenades etc).