It depends on what you mean by “handle”.
The Internet routing tables currently carry a little under 1M IPv4 prefixes (plus several hundred thousand IPv6). I do not know if the ISR 4331 can handle a BGP RIB of that size, but I imagine that it could, given enough RAM. But why would you need to carry the full routing table? If you are connecting to only a single ISP, then there probably is not any reason to have anything more than a default route to that ISP in the 4331, which of course it can handle.
From a BGP standpoint, I believe it comes down to how many ISPs will you connect to and what policies will you put in place to select the advertised routes from one ISP over another? The answer to that will have implications for your RIB size and the CPU cycles required to filter ingress & egress prefixes and maintain the FIB. Beyond BGP, there are questions of the resilience of your peering platform: If Internet connectivity is business-critical, should your standalone platform have as much redundancy as possible (eg, PSUs, fan trays, RPs, etc). IIRC, the 4331 only supports redundant power.
Disclaimer: I am long in CSCO
