No overflow 'might' be an issue. If your cooling system has a weak spot in it somewhere, you'll find out the minute the engine gets put through a bit of stress. I've bought 2 radiators online from ebay and both were GARBAGE. Alloy cores with plastic tanks. Mounting holes didn't line up, overflow port in the filler was almost sealed up, tank seals leaked, cores were different sizes... everything that shouldn't happen on a '100% pressure tested and checked' product. There are filler adapters that go in the top radiator hose - some have an overflow barb on them but this is a kinda ghetto way to fix the issue. There are also weld on overflow and cap assemblies for custom style radiators. You'd have to know someone who could weld one on and that is a pain too.