timed modeless dialog

Yes, create an Activity with style Theme.Dialog. This is a normal activity which looks like a dialog, while being modeless and accepting events.

An example:

<activity android:name=".activity.dialog.PhotoDialog"
          android:label="@string/photo_dialog_title"
          android:theme="@android:style/Theme.Dialog"/>

Edited:

Indeed Theme.Dialog blurs the underlying activity and makes it unaccessible. I had a similar requirement here I had to show upload progress dialog with text and cancel button. The main catch is in setting WindowManager.LayoutParams.FLAG_NOT_TOUCH_MODAL and resetting WindowManager.LayoutParams.FLAG_DIM_BEHIND.

Created a Dialog with custom content:

    if (progressDialog == null) {
            progressDialog = new Dialog(activityRequestingProgressDialog);
            progressDialog.requestWindowFeature(Window.FEATURE_NO_TITLE);
            progressDialog.setContentView(R.layout.progress_upload);
            progressBar = (ProgressBar) progressDialog.findViewById(R.id.progressBar);
            progressText = (TextView) progressDialog.findViewById(R.id.progressText);
            progressText.setText("0 %");
            progressText.setTextSize(18);
            Button buttonCancel = (Button) progressDialog.findViewById(R.id.btnCancel);
            buttonCancel.setOnClickListener(new View.OnClickListener() {
                public void onClick(View view) {
                    cancelProgressDialog();
                    stopUpload("Upload cancelled.");
                }
            });
            Window window = progressDialog.getWindow();
            window.setFlags(WindowManager.LayoutParams.FLAG_NOT_TOUCH_MODAL,
                    WindowManager.LayoutParams.FLAG_NOT_TOUCH_MODAL);
            window.clearFlags(WindowManager.LayoutParams.FLAG_DIM_BEHIND);
            window.setGravity(Gravity.BOTTOM);
            progressDialog.show();
        }

        progressText.setText(text);
        progressBar.setProgress(percent);

And this is the layout for this Dialog:

<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
          android:id="@+id/progressDialog"
          android:orientation="vertical"
          android:layout_height="wrap_content"
          android:layout_width="wrap_content"
          android:layout_centerVertical="true">

<TextView android:layout_width="wrap_content"
          android:layout_height="wrap_content"
          android:layout_gravity="center"
          android:textSize="18sp"
          android:padding="10dp"
          android:text="@string/progress_title"/>

<LinearLayout android:id="@+id/progressDialog"
              android:orientation="horizontal"
              android:layout_height="wrap_content"
              android:layout_width="wrap_content"
              android:padding="10dp"
              android:layout_centerVertical="true">

    <ProgressBar android:id="@+id/progressBar"
                 android:layout_width="150dp"
                 android:layout_height="34dp"
                 android:paddingRight="10dp"
                 android:max="100"
                 android:progress="0"
                 android:fadingEdge="vertical"
                 style="?android:attr/progressBarStyleHorizontal"/>

    <TextView android:layout_width="wrap_content"
              android:layout_height="wrap_content"
              android:layout_gravity="center"
              android:id="@+id/progressText"
              android:paddingRight="10dp"/>

    <Button android:layout_height="40dp"
            android:layout_width="80dp"
            android:id="@+id/btnCancel"
            android:text="@string/dialog_cancel"/>

</LinearLayout>
</LinearLayout>

just add FLAG_NOT_TOUCH_MODAL flag to your dialog

dialog.getWindow().addFlags(WindowManager.LayoutParams.FLAG_NOT_TOUCH_MODAL);