Pandemic Assistance for Student Veterans Act of 2020 This bill addresses the administration of educational assistance programs of the Department of Veterans Affairs (VA) in relation to the COVID-19 emergency, Specifically, the VA must provide educational assistance, including housing stipends and allowances, to individuals who are negatively affected by the COVID-19 emergency. The bill ensures that entitlement to educational assistance will not be charged or counted against the aggregate period in situations where an individual was unable to complete a course or program due to the COVID-19 emergency. The VA must treat an individual's withdrawal from a program of education due to COVID-19 between March 1, 2020, and December 21, 2021, as a mitigating circumstance and not charge the individual's educational assistance entitlement. The bill modifies the time limitation for use of Montgomery Bill benefits or vocational rehabilitation benefits during the pandemic so the window of eligibility does not expire during the COVID-19 emergency. Additionally, the bill adjusts the administration of certain benefits for veterans participating in an apprenticeship or other on-job training during the period between March 1, 2020, and December 21, 2021, including by proportionately reducing the 120-hour monthly training requirement to reflect an individual's period of unemployment without a reduction in training assistance. The bill expands educational assistance to include programs or courses of education at training establishments (e.g., establishment providing apprentice or other on-job training) during the COVID-19 emergency.