Can terminal enols be reduced by using LiAlH4?
Not only can that enol easily tautomerize to the aldehyde, the aldehyde is the major component at equilibrium at room temperature (by a lot!). The equilibrium constant for the similar system of ethanal/vinyl alcohol (one carbon shorter than yours) is $K \approx 3\times 10^{-7}$ (source: Wikipedia page on keto-enol tautomerism):

$$\ce{ CH3CHO &lt;=&gt; CH2=CHOH}\\
K = \dfrac{[\ce{CH2=CHOH}]}{[\ce{CH3CHO}]}\approx 3\times 10^{-7}$$ 

Thus, for every molecule of enol in this system, there are $\sim 3 \times 10^6$ molecules of aldehyde. $\ce{LiAlH4}$ will reduce the aldehyde and then LeChâtelier's principle will drag the enol along for the ride.