It seems, based on some experimental work done on the International Space Station and published recently in the journal Astrobiology, that the answer is yes. Fungi are eukaryotes and posses cell walls made partially of chitin, a polymer of acetylated glucose that also comprises arthropod exoskeletons. In this experiment, endolithic Antarctic fungi and dried colonies were subjected to 18 months of simulated martian conditions; upon return and rehydration, the scientists evaluated whether the cells were viable - could they grow once more now that conditions were more luxurious? About 10% of the cells proved viable, compared to roughly 50% of control cells that were kept in a dark Earth-based laboratory. Intact DNA was recovered from about 75% of endolithic fungi, but just 10-15% of fully exposed organisms. While the work shows that martian conditions are tolerable to some organisms and confirms the importance of radiation shielding in the form of rock-hosted habitats, it doesn't necessarily offer fundamentally new hope of encountering life on Mars. For one thing, martian soil chemistry is likely more treacherous than Antarctic sandstone, given photochemical reactions and free radical production. And metabolic activity - a prerequisite for doubling and a vibrant, sustainable biosphere, was not assessed. Cell and DNA survivability studies under martian conditions would perhaps be more useful in determining the likelihood of remnant biochemicals. Abstract for the paper below:

Dehydrated Antarctic cryptoendolithic communities and colonies of the rock inhabitant black fungi Cryomyces antarcticus (CCFEE 515) and Cryomyces minteri (CCFEE 5187) were exposed as part of the Lichens and Fungi Experiment (LIFE) for 18 months in the European Space Agency's EXPOSE-E facility to simulated martian conditions aboard the International Space Station (ISS). Upon sample retrieval, survival was proved by testing colony-forming ability, and viability of cells (as integrity of cell membrane) was determined by the propidium monoazide (PMA) assay coupled with quantitative PCR tests. Although less than 10% of the samples exposed to simulated martian conditions were able to proliferate and form colonies, the PMA assay indicated that more than 60% of the cells and rock communities had remained intact after the “Mars exposure.” Furthermore, a high stability of the DNA in the cells was demonstrated. The results contribute to assessing the stability of resistant microorganisms and biosignatures on the surface of Mars, data that are valuable information for further search-for-life experiments on Mars.