A 275/45R18 is approx 740mm in overall diameter (OEM tyre is ~675mm in OD). You are raising the rear by ~32mm and will need at least 4.08:1 diff ration to maintain the same gearing.
Gears on top of the drag radials you've mentioned will only result in similar acceleration - yes, you might gain a little from grippier tyres but that only if you get wheelspin now - because grippier tyres will assist in eliminating lost time in wheelspin.
The drag tyres on their own will slow your quarter-mile pass times as you are increasing the gearing, not decreasing.
If you are going to use the drag tyre, you'll need 4.3 or 4.4 gears to gain an acceleration advantage and them when you fit standard size rear tyres, at 60mph, you'll be pulling over 3000rpm in 6th gear.
Depends what you want really. If its a DD, then cheapest is 275/35R18 rear with 245/45R18 front. This gives you ~8% lower gearing without changing diff gears.
If the car is a competiton car and you want tot go balls-out in toerms of chasing 1/4mile times, and you want to use a sticky drag tyre and use the size you;ve mentioned, then you need 4.3 or 4.4 gears to gain improved acceleration (IMHO)
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