Is there a drain at the bottom of the hydraulic tank?

Confirmed both facts. Now finalizing revised answer.

Yes, the 270D LC hydraulic tank has a factory drain plug on the bottom. Deere's parts catalog lists hex-socket drain plug part 9134109, a hexagonal socket head drain plug fitted to the 270D among other models, so it's a designed drain point, not something you improvise by cracking a hose. The tank sits under the upper structure with the reservoir cap/sight gauge and suction strainer accessible from the top for service.

That said, a full oil change is a bigger job than just pulling that plug. Per Deere's published spec sheet, total Hydraulic System capacity is 74 gal. (280 L). The tank drain only empties the reservoir itself; a large share of that oil stays trapped in the cylinders, hoses, valve bodies, and pump housing, none of which drain through the tank plug alone. So don't expect a full 74 gallons to come out the bottom fitting, and plan the procedure around that.

Practical procedure to get the most oil out without pulling every hose:

1. Run the machine to warm the oil (thins it, drains faster), then shut down and relieve pressure by cycling all controls with the engine off, key on.
2. Position a drain pan under the tank drain plug, remove it, let the tank gravity-drain fully. Pull and clean the suction strainer while it's open, that's standard practice whenever the hydraulic oil is changed on this machine.
3. Change the hydraulic filter element(s) now while everything is open.
4. To purge more of the old oil from cylinders and lines: fully retract/extend every cylinder several cycles before draining (pushes trapped oil back toward the tank), then after refilling, run the machine and cycle every function (boom, arm, bucket, swing, travel) for several minutes, recheck, and top off, since the lines and cylinders will draw fresh oil out of the tank as they refill.
5. If the old oil was contaminated (water, metal, varnish) rather than just aged, a single drain-and-refill won't fully dilute what's sitting in dead-leg lines. Running a filter cart for a few passes, or doing a second drain-and-refill after a few hours of operation, gets you much closer to a full clean fill than one pass.

Refill with Deere-spec hydraulic oil (check your operator's manual for the correct viscosity grade for your climate) and verify final level with all cylinders retracted per the sight gauge on the tank.