Electromagnetic waves in the ion-cyclotron (IC) range of frequencies are presently investigated as possible current drive (CD) systems in fusion reactors. Among many physical and technical issues, an accurate description of radio-frequency (RF) power absorption by fusion-born alpha particles is of special importance, since RF heating of these particles is not only detrimental for the CD efficiency, but might worsen the operative conditions by increasing their prompt losses. The capability of the full-wave TORIC code has been recently augmented to account for RF absorption by fusion-born alpha particles, calculated to all-orders in finite Larmor radius and with a realistic distribution function. Here, we present simulation with TORIC addressing the sensitivity of current drive efficiency on the design of a future reactor, in particular density and temperature profiles, magnetic field intensity, and plasma dimensions. For this purpose, we have investigated possible frequency windows for CD for two proposed versions of the DEMO reactor, namely its pulsed and its more ambitious steady-state design. The important role of the antenna for a realistic estimate of the CD efficiency is pointed out.