Basic answer: Yes, they can survive, but only if they do not need to undergo cellular respiration. I quote from Microbiological Research, Volume 169, Issue 2-3, p. 185-195:
Mitochondrial DNA (mtDNA) is a compulsory genetic component for encoding essential respiratory enzymes in all eukaryotic cells.
In other words, for cellular respiration to occur, the yeast must have the mtDNA. However, the article goes on to explain,
However, some yeast species (called rho positive) could survive without mtDNA under conditions of fermentation (a metabolic pathway alternative to respiration). In these species, partial or complete losses of mtDNA (spontaneous or induced by mutagenic factors) is associated with the formation of respiratory deficient mutants (rho− type or rho0 type) characterised by slow growth on fermentable carbon sources (e.g. glucose) and inability to grow on non-fermentable sources, such as glycerol or ethanol.
In other words, yeast can survive in the presence of correct conditions for fermentation to occur. In the absence of those conditions, the yeast must have the mitochondrial DNA, because in order for it to survive, it must perform cellular respiration.