Can worldspace UI Elements cast a shadow?

It definitely used to be possible, but after some quick tests it would appear that the shadow system auto-culls all UI (for good reason), making shadow-casting essentially impossible. The only real way to do this would be to use actual renderers. For text, the legacy 3D text-mesh component still works, so you can apply a custom shader and material to it to cast shadows. Here's a shader that will do that;

 // Unity built-in shader source. Copyright (c) 2016 Unity Technologies. MIT license (see license.txt)
 
 Shader "GUI/Shadowed Text Shader" 
 {
     Properties 
     {
         _MainTex ("Font Texture", 2D) = "white" {}
         _Color ("Text Color", Color) = (1,1,1,1)
     }
 
     SubShader 
     {
         Tags {
             "Queue"="Transparent"
             "IgnoreProjector"="True"
             "RenderType"="Transparent"
             "PreviewType"="Plane"
         }
 
         Cull Off
 
         Pass 
         {
             Lighting Off ZWrite Off
             Blend SrcAlpha OneMinusSrcAlpha
 
             CGPROGRAM
             #pragma vertex vert
             #pragma fragment frag
             #pragma multi_compile _ UNITY_SINGLE_PASS_STEREO STEREO_INSTANCING_ON STEREO_MULTIVIEW_ON
             #include "UnityCG.cginc"
 
             struct appdata_t 
             {
                 float4 vertex : POSITION;
                 fixed4 color : COLOR;
                 float2 texcoord : TEXCOORD0;
                 UNITY_VERTEX_INPUT_INSTANCE_ID
             };
 
             struct v2f 
             {
                 float4 vertex : SV_POSITION;
                 fixed4 color : COLOR;
                 float2 texcoord : TEXCOORD0;
                 UNITY_VERTEX_OUTPUT_STEREO
             };
 
             sampler2D _MainTex;
             uniform float4 _MainTex_ST;
             uniform fixed4 _Color;
 
             v2f vert (appdata_t v)
             {
                 v2f o;
                 UNITY_SETUP_INSTANCE_ID(v);
                 UNITY_INITIALIZE_VERTEX_OUTPUT_STEREO(o);
                 o.vertex = UnityObjectToClipPos(v.vertex);
                 o.color = v.color * _Color;
                 o.texcoord = TRANSFORM_TEX(v.texcoord,_MainTex);
                 return o;
             }
 
             fixed4 frag (v2f i) : SV_Target
             {
                 fixed4 col = i.color;
                 col.a *= tex2D(_MainTex, i.texcoord).a;
                 return col;
             }
             ENDCG
         }
 
         Pass 
         {
             Tags { "LightMode" = "ShadowCaster" }
 
             CGPROGRAM
             #pragma vertex vert
             #pragma fragment frag
             #pragma target 2.0
             #pragma multi_compile_shadowcaster
             #pragma multi_compile_instancing // allow instanced shadow pass for most of the shaders
             #include "UnityCG.cginc"
 
             struct v2f 
             {
                 V2F_SHADOW_CASTER;
                 float2  uv : TEXCOORD1;
                 UNITY_VERTEX_OUTPUT_STEREO
             };
 
             uniform float4 _MainTex_ST;
 
             v2f vert (appdata_base v)
             {
                 v2f o;
                 UNITY_SETUP_INSTANCE_ID (v);
                 UNITY_INITIALIZE_VERTEX_OUTPUT_STEREO (o);
                 TRANSFER_SHADOW_CASTER_NORMALOFFSET (o)
                 o.uv = TRANSFORM_TEX (v.texcoord, _MainTex);
                 return o;
             }
 
             uniform sampler2D _MainTex;
             //uniform fixed _Cutoff;
             uniform fixed4 _Color;
 
             float4 frag (v2f i) : SV_Target
             {
                 fixed4 texcol = tex2D (_MainTex, i.uv);
                 clip (texcol.a* _Color.a - 0.5);
 
                 SHADOW_CASTER_FRAGMENT (i)
             }
             ENDCG
         }
     }
 }

Unfortunately, this won't work straight up because the TextMesh system assumes you are using the auto-generated font material. To get it working properly, you'll also need to attach this script;

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 [RequireComponent(typeof(TextMesh)), ExecuteInEditMode]
 public class ShadowTextSetup : MonoBehaviour
 {
     private TextMesh textMesh;
     new private MeshRenderer renderer;
 
     public Texture fontTexture { get; private set; }
 
     private void OnEnable ()
     {
         if (!TryGetComponent<TextMesh>(out textMesh) || !TryGetComponent<MeshRenderer>(out renderer))
             return;
 
         fontTexture = textMesh.font.material.GetTexture ("_MainTex");
         renderer.sharedMaterial.SetTexture ("_MainTex", fontTexture);
     }
 }