Can I extend icemaker line by joining two braided lines?
&quot;Would you do it the same way or would you go copper?&quot;

I would run 1/4&quot; copper tubing from the shut-off valve at the water source all the way to the wall behind the refrigerator; that line I would then consider a permanent install. This is especially appropriate if the line runs through/behind cabinets or other semi-inaccessible areas.
At the wall behind the refrigerator I would install an inline valve (to provide a quick local shut off capability) and transition to braided stainless-steel jacketed hose.
NOTES:

copper tubing compression fittings are pretty reliable
any hose (braided line is just a hose...) should be used only in areas where a leak could be easily noticed and the hose easily replaced
valves are often the weak point; do not use a &quot;saddle valve&quot; at the water source, and expect to replace any in-line valves, especially needle-valves.