Not so much,

    >>> s="1"+"0"*4300
    >>> json.loads(s)
    ...
    ValueError: Exceeds the limit (4300 digits) for integer string conversion: 
    value has 4301 digits; use sys.set_int_max_str_digits() to increase the limit

Relevant discussion: https://news.ycombinator.com/item?id=32753235

Your sibling comment suggests using decimal.Decimal which handles parsing >4300 digit numbers (by default).

This should be interpreted as a stop-gap measure before a subquadratic algorithm can be adopted. Take a look at _pylong.py in new enough CPython.