YES! Primary cosmic rays can be antiprotons and antinuclei. Antiprotons where E>1.8GeV make up about 0.1% and antinuclei where Z \geq 2 not more than 0.23%. So total around 0.1% to 1% maximum.
Original data from Aizu,H et al Physical Review vol116, p436 (1959) and Jain,P.L., Lohrman, E. and...