@yodakramer Check out the kettlebell thread:
Personally I use both the SYSTM strength and also add my own lifts with weights - mostly upper body. I would recommend putting your SYSTM plan together with strength so that the training load is balanced appropriately. Then you can either do strength and add your own lifts or just substitute the strength sessions for different lifts.
Go slow - it is easy to overdue it and compromise your performance on the bike.
Also my take on the SYSTM strength training is that it is really focused on the strength and stability necessary for the bike (eg. Strong core to better transfer power, single leg squats for better power generation, etc. ) and not more than that.