If you're wanting to apply 4#/yr to your lawn then no, applying a liquid vs granular should not change your total nitrogen inputs. Total nitrogen applied is the same no matter if you add the water previous to or after application. Eventually it all needs to become liquid in order to enter the soil & plants' ecosystem. Now whether you need to apply 4#N/yr is a different question, and applying liquid vs granular may make that more obvious.
My argument is that when we apply that granular 1#N every 6-8 weeks, as typical, it tends to be a bit of an over application to account for loss, etc. Assuming you use a good controlled-release nitrogen product the release period should be what you're expecting; approx 6 weeks. 1#N over that 6wk period is approx 3/4#N/month which, from my gleanings is more than most residential turfgrass needs for normal growth. But even if you do want to go a bit heavy-handed you'd need to do so with a controlled-release granular, not 46-0-0 Urea like you mention. 46-0-0 will probably have a release period of 3-4 weeks, so applying 1#N of straight Urea will end up giving you surge growth during the heavy release period (meaning more mowing) and a reduced effect the last half of the period. Ideally you would apply 1/2#N every 3-4 weeks, but doing such low rates with granular 46-0-0 Urea can be a bit tricky. That's where liquid comes in. Since you're a bit limited by not having irrigation you'll have to limit yourself to more frequent 1/4#N apps, as you mention (or time it ahead of gentle rain events, if at all possible). But if spraying you find you'll only do so when the turf is in need of it and the turf has growth potential. I liken it a bit to those automatic animal feeders that throw down a set amount of food no matter if the weather or circumstances deem it needed. Whatever gets wasted and lost is the price to pay for the convenience of setting it and forgetting it. Same idea here - if you go the liquid route you'll have such a close eye on the truf that you'll start recognizing when the turf needs fed and when it's good. You may be surprised how one or two apps per month may just suffice, hence reducing your total yearly N.
Long explanation but it's been something I've noticed since I've gone the liquid route.
BTW, look into the idea of a Hybrid approach if at all possible. If you can find a good slow-release fertilizer to feed & stimulate the soil ecosystem, supplying the base layer of nutrition, your liquid apps then become supplemental. It allows for some flexibility on application timing as well since spraying every 2 weeks can become old real quick!