Yes, the antenna would lean forward quite a bit. This may look funny, but it will have surprisingly little effect on how well the antenna works.
Let's work a few examples.
Suppose, for example, that the antenna is leaning straight forward at 45 degrees. How will this affect its radiation? Consider, first, radiation in the forward direction. The signal strength in the forward direction will be reduced, of course -- by the cosine of the angle of lean. Suppose that we assume a certain strength S in the forward direction for a perfectly vertical antenna; then the same antenna leaning forward 45 degrees will radiate a signal with strength (S cos 45) or 0.707S. That is, because of the forward lean it will be as if you were running, say, 35 watts instead of 50 watts. That's a loss of about 1.5 dB, about 1/4 of an S-unit. Negligible!
How about radiation to the right or left side? The radiation to either side will be exactly as strong, with the antenna leaning forward 45 degrees, as it would be with the antenna perfectly vertical, no loss at all. However, the signal to the side will no longer be vertically polarized, and the receiving antenna at the other end (probably on a repeater) is vertical. This also reduces the received signal by the cosine of the angle, so that, too, will be like running 35 watts instead of 50, about 1.5 dB weaker. Negligible!
Radiation to the rear? Same as to the front! The signal will probably be weaker there, though, because the antenna is so placed that the truck is in the way. But that would be true no matter the angle of lean; any effect will be caused by the antenna's location, not by its angle.
All of that is for an antenna leaning forward 45 degrees. How about other angles? Here's the result for a few different angles:
10 degrees: 0.06 dB, 1/100 of an S-unit
20 degrees: 0.27 dB, 1/40 of an S-unit
30 degrees: 0.62 dB, 1/10 of an S-unit
45 degrees: 1.5 dB, 1/4 of an S-unit
60 degrees: 3 dB, 1/2 of an S-unit
75 degrees: 5.87 dB, just less than 1 S-unit
So you can see that leaning the antenna has astonishingly little effect on the transmitted (or received) signal strength unless it's nearly horizontal.
All of that stuff assumes that the other guy's antenna is at the same altitude as yours. What about repeaters? Their antennas are higher. Radiation at upward angles is affected not only by the elevation from horizontal, but also by reflections from the ground. The analysis is a little more complex, but the results are similar, and the effect of a non-vertical antenna is similarly negligible.
So, you need not worry if the antenna is mounted so that it leans, unless the appearance is bothersome. Maybe you could mount two antennas, one on the right side of the hood and one on the left side, with one hooked up and the other not, and put tennis balls on the tips. Then you'd look like the Orkin Man!