As @Gi_T has already mentioned my recommendation is to follow Hugo Zanini’s amazing write up on how to retrain YOLO so that you can recognize custom objects and export that resulting model to TensorFlow.js. He walks you through each step in a nice easy way that you should be able to follow which will allow you to use the resulting model via TensorFlow.js in the browser - but as you mentioned does involve a Python pipeline at the start for the purpose of retraining before you convert it over.
Our native TFJS COCO-SSD model has frozen weights and is not suitable for re-training.
On the subject of if it is possible in JS - the short answer is yes, but we are a much younger team than TF Python so we need more people like you to create the examples of tomorrow  An exciting time to be involved as we grow (3x in the last year alone) so now is a great time to grow with the community!
Let us know how you get on! Would love to see more TensorFlow.js examples like Hugo’s out there too but natively in JS. We support Node.js for server side training - and the pre/post processing can be accelerated faster than Python due to the JIT compiler of JS so you may even see some perf boosts there too.
Our community is growing fast so I am sure someone will implement something natively in the not too distant future. If there are any takers reading this please do go for it and tag me if you make it so we can feature you