When using NFC peer-to-peer communication (aka Android Beam) between two Android (4.0+) devices, there is no way to avoid the Beam UI. So it is not possible to transfer data without the "Touch to Beam".
Before Android Beam (effectively Android 2.3.3-2.3.7), this was possible through foreground NDEF push (which is now (a) deprecated and (b) on Android 4.0+ implemented through Beam). In that case NDEF messages where immediately transfered without the "Push to Beam" window.
Only starting with Android 4.4, there is the possibility to communicate between two Android devices over NFC without the Beam UI (actually without using Android Beam and peer-to-peer mode at all): If both devices are 4.4+, one device can use Android HCE to emulate a contactless smartcard and one device can use the reader-mode API (this only works with the reader-mode API introduced in 4.4, so both devices need to be 4.4+) to communicate with the emulated smartcard.