Not exactly. I'm assuming that long run people will adjust to higher oil prices just like they did before, and in the short run GDP will drop/flat-line then increase, just like it did before.
Short run during the late seventies/similar price run ups the nation went from vehicles that average ~12mpg to many smaller offerings that could easily average ~30-50mpg while US GDP stayed flat or declined. Some of these cars are around today, so clearly there was the capital needed for investment. The only significant impact on investment is when the consumer does not change their level of consumption, diverting a proportional amount of wealth away from other economic sectors to keep pace with rising fuel costs. Clearly the consumer has reached the point where that isn't the case, and consumption has consistently dropped for the first time in decades. The shift in spending is even reflected in used car prices, with econoboxes that would've been lucky to go for a few hundred before the oil price run up appreciating
several hundred percent, possibly into the thousands (percent) in extreme cases.
Attitudes and consumption changes, it simply takes time, and initially, just like it did last time, GDP takes a hit while consumers adjust. Even on the new vehicle front there are plenty new fuel efficient vehicles to reflect demand in that market. Aptera currently makes the cheapest (long run) new enclosed vehicle and has an entire years worth of pre-orders unless they ramp up production somehow, Toyota's supposedly set to come out w/ three new versions of the Prius, one of which may be a plug-in, Honda's supposedly coming out w/ a lower cost hybrid, which are all besides the point since most manufacturers offer relatively low cost (~$12-15k) vehicles that can easily see ~35-45mpg if driven conservatively.
For the people who can afford new vehicles, they'll have less capital, but will also tend to spend the same or less on a more fuel efficient vehicle. People who can't afford new vehicles will instead buy more fuel efficient used vehicles. More will take mass transit, and so on. In terms of renewables it tends to be cheaper to invest in them long run for everyone but the fossil fuel supplier and friends, but change takes time and current industries have plenty of leverage. I figure the price can't climb much about ~$200-300/bbl w/o alternatives looking too good to pass up. Even w/ oil prices at a hundred EVs in countries with much higher taxation look like slam dunks, and I wouldn't go so far as to assume that the oil producing countries aren't watching what happens.