Not much, altough maybe now with the current situation it will take a bit longer for HR coordination.
If you are fering if the contract would be withdrawn, I think is very unlikely.
Once the offer is extended, it would be EXTREMLY rare that it gets rescinded.
What seems clear by now is that this is truly harming economy, and in the next weeks we will see whether we are heading to a global economic recession. If this is the case, and we indeed face a global recession -even if not as hard as the previous one-, this will have an impact in consulting. Why? Simply because there would be less clients, less engagements with the usual clients, and an overall freeze in spending.
This, for sure, will impact recruiting, reducing the classes of BAs and Associates for a couple of years.However, this won´t affect you if you are "in" already.
Hope it helps!