What are the implications of connecting lithium battery packs in series?
The concern with series-connected batteries of any type is uneven charge/discharge rates within the string of cells.  This can cause overcharging of some cells, which can lead to premature cell failure and it can also lead to reverse charging during discharge which can also lead to cell failure.
The entire purpose of BMS systems is to keep track of the individual cells in the pack and ensure that they are kept balanced at all times.  This maximizes cell life and reduces the possibility of cell failure happening.
You should not connect independent battery packs but rather should put together a cell pack you need with an appropriate battery management systems that can control all the cells in the pack.
Can you do what you are proposing?  Sure, there is nothing stopping you.
Is it a good idea?  Not really since this will almost certainly reduce the lifetime of your battery packs.
Can this cause damage?  Yes it can, cells can burst making a mess and possibly causing damage to enclosures or things nearby.  It is possible that cells can  discharge rapidly causing heating and possibly fire.
It's always best to use LiIon chemistry batteries properly to reduce the possibility of problems.