No they do not drop dragon scimatars because even a rune scimitar is considered a rare drop from a cockarach monster and dragon scimitars are "MEMBERS ONLY" item.
The level 83 cockroach soldiers drop them on occasions in runescape, for nonmembers and members.
They drop is after about 15-25 cockroaches. Don't be sad though. They also drop rune square shields and a huge amount of Mithril ore (in paper). (this is in f2p) (i don't know in p2p)
The best way to get 60 attack is to probably train on cockroach soldiers (lv 83). not only that, they drop rune scimitars, rune square shields, laws, deaths, and lots of other cool stuff.
There are only a few. The best drop is the adamant med helm so this is not recommended. Attacking Cockroach Soldiers are better as they drop Rune Scimitars and Sq. Shields. Note: It may take about 15 kills to get a good item. Most of the time the drops are coins.
You can make one, at a high smithing level (not recommended, since you lose money on most smithing activities). Also (from runescape.wikia.com): "Free players are able to obtain the rune scimitar as a semi-rare drop from Cockroach soldiers in the Stronghold of Player Safety. For members, the rune scimitar can be obtained as a fairly common drop by a variety of monsters, such as Zamorak warriors and Fire giants."So, it seems that for free players, the cockroach soldier is your only option. Of course, you can simply buy one at the Grand Exchange.
Cockroach Soldiers drop a wide variety of items in RuneScape and have since been less killed as a better alternative, Grotworms, has opened up after a recent update. Cockroach Soldiers now always drop Carapace, which can be crafted for crafting experience. Cockroach Soldiers do have access to the rare drop tables, but offer fairly invaluable regular drop items and therefore are not killed as commonly any more due to newer and better monsters.
the drop rate is on chance but i belive it is a rare drop from them
considering anchous can weaken you and i forget they might be aggressive i would go with cockroach soldiers and plus cockroach soldiers can drop rune scimitar witch sell for around 30k right now.
* Cockroach workers * Cockroach soldiers * Ankous * Catablepons * Dark Wizards * Ice Warriors * Ice Giants * Moss Giants * Hill Giants
From the grand exchange, but in nonmembers world the cockroaches (the higher levels) drop rune scimitars once in a while. Otherwise in members world once you did monkey madness you can buy dragon and rune scimitars.
I do not know the complete list however, I do know that these monsters do drop law runes: barbarians dark wizards wizards cockroach soldiers
A huge amount of monsters drop rune scimitars in runescape, the most popular one being Cockroach Soldiers (for free players)For members, most rune scimitars are obtained from zamorak warriors and fire giants, or even metal dragons!