That has been tried unsuccessfully with two Caseta SmartBridge Pro’s in the past. The delay is caused by the Pico remote transmitting for about a full second, hogging the Lutron Clear Connect RF frequency.
Thus, a RadioRA 2 Main Repeater is required as it allows its frequency to be changed. But one has to take and pass a free online training class in order to be able to configure a RadioRA 2 Main Repeater.
For UK based folks: You need to create a Lutron Account and choose US when creating this, you can then access the RadioRA2 L1 training.
The solution proposed (changing frequency) works. I was able to pick up a RadioRa2 European Main Repeater for 50GBP from ebay for picos and have my dimmers running on my main RA2 Select system.
You need a MyLutron account and then go to the training site called 'LCI online'. My guess is that you'll need to choose USA training as RadioRA 2 is not a UK/European product. Search for 'LP 620 - RadioRA 2 Level 1 Online Training'.