Blood pressure (BP) is a key indicator of cardiovascular health. As hypertension remains a global cause of morbidity and mortality, accurate, continuous, and non-invasive BP monitoring is therefore of paramount importance. Photoplethysmography (PPG) and electrocardiography (ECG) can potentially enable continuous BP monitoring, yet training accurate and robust machine learning (ML) models remains challenging due to variability in data quality and patient-specific factors. Recently, multiple research groups explored Electroencephalographic (EEG)--based foundation models and demonstrated their exceptional ability to learn rich temporal resolution. Considering the morphological similarities between different biosignals, the question arises of whether a model pre-trained on one modality can effectively be exploited to improve the accuracy of a different signal type. In this work, we take an initial step towards generalized biosignal foundation models by investigating whether model representations learned from abundant EEG data can effectively be transferred to ECG/PPG data solely with fine-tuning, without the need for large-scale additional pre-training, for the BP estimation task. Evaluations on the MIMIC-III and VitalDB datasets demonstrate that our approach achieves near state-of-the-art accuracy for diastolic BP (mean absolute error of 1.57 mmHg) and surpasses by 1.5x the accuracy of prior works for systolic BP (mean absolute error 2.72 mmHg). Additionally, we perform dynamic INT8 quantization, reducing the smallest model size by over 3.5x (from 13.73 MB down to 3.83 MB) while preserving performance, thereby enabling unobtrusive, real-time BP monitoring on resource-constrained wearable devices.