Is an improvised weapon treated as similar enough to a weapon to use its properties still considered "improvised"?

Question

In PHB, the 2nd paragraph of the description of Improvised Weapons (p. 147) states:

In many cases, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the DM’s option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus.

If I am understanding this correctly, then the mentioned table leg (or similar object) can be treated as a club. If that is correct, then it would have the light property, as the club has it. If that is also correct, that would mean I can wield a light weapon in one hand and an improvised club-like weapon in other hand, and use Two-Weapon Fighting with those, as both are light.

If all of that is still correct, then can an improvised weapon that is similar enough to a real weapon - e.g. a table leg used as a club - still be treated as an improvised weapon for the purpose of the last bullet point in the Tavern Brawler feat (PHB, p. 170)?

Specific scenario that I am wondering about: I wield a Scimitar (a light weapon) in one hand and a table leg (treated as a club, so also light) in the other hand. On my turn, I attack with the table leg as my Attack action. Then one of two things happen:

1. I miss - then, as both wielded weapons are light, I proceed to attack with my scimitar (per Two-Weapon Fighting)

2. I hit - then I drop one of my weapons to free one of my hands and attempt to grapple the target.

Of course this is assuming that I have the Tavern Brawler feat, which states:

• You are proficient with improvised weapons.
• Your unarmed strike uses a d4 for damage.
• When you hit a creature with an unarmed strike or an improvised weapon on your turn, you can use a bonus action to attempt to grapple the target.

Does all of that work as I've described, or is there somewhere a flaw in my reasoning?

Answer 1

Yes, it is still improvised

You are correct that an improvised weapon is still an improvised weapon, thus you still have the option to grapple the target with your bonus action.

At the DM’s option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus.

It is still an improvised weapon, but can be treated as a similar weapon (a club), if your character is proficient with it. So it has both the properties of an improvised and the similar weapon.

Note: This treatment also has two conditions attached: at DM's discretion, and only if the they are proficient with said weapon. Most (if not all) characters are proficient with simple weapons, however.

In short:

1. If you miss with the table leg, then you can use your bonus action only to attack with the scimitar.
2. If you hit with the leg table, then you can use your bonus action to either attack with scimitar, or grapple the target.