Any jet with full trust and 10 degrees pitch up will climb away.
I had an unreliable airspeed in IMC take off in a A310;bit scary but came on top at 10,000', at which point the pitot tube cleared and things got normal. Just a whole bunch of warnings regarding slats and flaps.
Also I remember towing gliders for a whole day with airspeed indicating '0'.
At the end of the day maybe it is easier to learn to fly than to remember al the patches people come up with and try to mold into SOP's.