Answer
It will sweat.
Work Step by Step
The vapor pressure $P_v$ of the air in the house is uniform throughout, and its value can be determined from $$
P_v=\phi P_{g @ 70^{\circ} \mathrm{F}}=(0.38)(0.3633 \mathrm{psia})=0.1381\ \mathrm{psia}
$$ The dew-point temperature of the air in the house is $$
T_{\mathrm{dp}}=T_{\text {sat } @ P_\gamma}=T_{\text {sat } @ 0.138 \text { lpsia }}=43.3^{\circ} \mathbf{F} \text { (from EES) }
$$ That is, the moisture in the house air will start condensing when the air temperature drops below $43.3^{\circ} \mathrm{C}$. Since the canned drink is at a lower temperature than the dew-point temperature, some moisture will condense on the can, and thus it will sweat.
