The history of the last 20 years suggests so. During this time, there's been a close correlation (0.67 in annual data) between the unemployment rate and public sector net borrowing as a share of GDP. On average a one percentage point rise in unemployment has added 1.4 percentage points of GDP to borrowing.
That said, borrowing this year looks likely to be higher than the unemployment rate would predict. Post-1993 relationships suggest that an unemployment rate of 7.8 per cent should be associated with borrowing of 5.4 per cent of GDP. But forecasters expect a deficit of around eight per cent, if we exclude the boost to the public finances given by the transfer of the Royal Mail pension plan. This might be a sign that there is a small “structural” budget deficit. However, as the idea of a structural deficit is at best imprecise and at worst unscientific nonsense, we should be sceptical of this. It might instead be that widespread labour hoarding and under-employment mean that the economy is weaker than measured unemployment suggests, and so you’d expect tax revenues to be weak and public spending high.